General
FWIW I teach martial arts to both kids and adults 5 days/nights a week, it is how I make my living, since you asked for advice I offer the following.
My daughter is currently becoming more and more disenchanted with her martial arts studies. She is 10 years old, is a 2nd degree black belt in Tang Soo Do-Moo Duk Kwan, and is on the cusp of earning her black belt in the Haidong Gumdo sword art. Her current instructor is a pretty good man, but he does seem to spout on about his political agenda and that can get very tiresome, where it tends to droan on into classes. He is currently shuffling around his class schedule to accomidate his adult students and eliminating some youth classes. She has been going to between 4-7 classes per week, and may have become a little burned out, as well. I have discussed options with her, and currently see something like 4 options:
1) Take classes with same school, different dojang (one other dojang is fairly close)
2) Change school, but same discipline to maintain rank (not sure if different schools would honor current ranking)
3) Start over with different martial art form (how hard to completely start from scratch?)
4) Quit completely (not my choice, or her's right now, but it is an option)
5) Simply tolerate her master's load of crap (she's losing much respect for him)
I don't know who has had an issue like this, with their kid or a student of theirs, but I would love some advice.
Regarding your options listed.
1) Are you saying there is an affiliated (sister) school nearby? If so this might be a decent option, but it could be hard for your daughter getting established in another school. Unless they know her or she has trained there before. While they might honor the rank, there is an established hierarchy within the school among the students already training there, there would be a period of adjustment for your daughter.
2) If the school is still the same discipline (style) then they might honor the rank after a trail period to evaluate your daughter. This should be something to discuss prior to having your daughter check out the school. However this isn't a bad option. My top student (junior that is, she's 14), came from a American Karate school that had a similar lineage (taught the same forms etc.etc. but I taught more of them) I accepted her at her current rank and didn't promote her till she had learned all of the forms, the way I taught them, for her next rank. While her parents had been training with me in a different art, she didn't want to come over and try out my classes. They gave her time and as she became dissatisfied with her classes she tried out mine, she's been with me 3 years now and just tested for 1st dan. BTW she started in the martial arts when she was five as well.
3) Starting over from scratch can be hard, but it can give her a different perspective as well. This year we just started a Junior Modern Arnis program for students 10 yrs and older. Four of my TKD students came over, two others trained in both arts. One of my big concerns was for the younger students (10-11) to adapt to a different art, taught differently, etc. etc. especially the advanced intermediates in my TKD program (they'd been training about 3 yrs in the TKD). They loved the art, adapted to it well and they accepted the "new" lower rank (in the JMA program they have to earn their white belt even) and have progressed nicely. However they all enjoy the new program. But giving up their rank to start in a different karate school which is basically the same as the MDK/TKD school you are going to might be hard to swallow for a 10 yr old 2nd dan.
4) This would suck, but it might loom on the horizon if the problem isn't corrected.
5) Frankly this should be the easiest to fix although it might not be. As the others have said and I totally agree this guy's politics have nothing to do with the time training on the floor, he needs to shut up. You are paying for the guy to teach your daughter martial arts, not political theory, he is a fool if he is doing this regularly on the training floor. I too will instruct my students especially my brown and black belts on different things, and I might get on a soap box, however it always relates to the martial arts, especially when I'm teaching on self defense issues. However I believe my students need to know that they can't do military knife work/defense and not expect to probably go to jail. They need to know you can't break a kids arm, or blind a kid, because they reached out to lay their hand on you etc. etc. So I tell them this again and again. But I don't ever discuss the government or my feelings on the laws etc. etc.
I would talk with the instructor, not as a the parent of one of his 2nd dans; but as a paying customer, who's daughter is getting frustrated with having to listen to his whiny crap. It is not right for you to pay money to hear this guy talk about big brother.
I do think that a break may be in order soon, however she is currently prepping for her black belt test in Haidong Gumdo, and wants to stay sharp in order to achieve this goal of hers. Afterwards, I'd be fine and dandy with a break from it all, but how long of a break would be appropriate for a kid this age? Are we talking a week, a month, a year? I don't want her burned out, but I don't want her to lose her passion for it either. Through it all, she still loves the martial arts.
As the others have said I think 4-7 classes per week is a bit much. My two students who train in both my TKD and Modern Arnis programs were going 4-5 classes a week one is 11 and one is 14; my normal students attend 3 (1 hour) classes in my TKD program; and 3 (2 classes at 1 1/2hrs, and 1, 1 hr) classes in my Modern Arnis program. They both got burned out, I didn't make them go, in fact I advised against it, but the kids wanted to and they kept up in both arts. To be fair the 14 yr old is now in 9th grade and snowed under in school work which is what is killing him. But the 11 yr old took a break for swimming at the end of the summer and has yet to be back.
I agree with everyone who says that a kid's childhood should be fun, which is why I teach kids in kids classes and not adults. In the kids classes I give them different warm up games etc. etc. and have a different view point on their skills. I teach them age appropriate self defense etc. etc. Still I sometimes feel that the kids are overwhelmed with band, music lessons, drama, foreign language school, competing in other sports (baseball, football, volleyball) as well as doing martial arts in my classes. I mean I have kids taking AP courses in school, doing home work in my classes while waiting for their classes to start. I'm not complaining in fact I'm honored that they still want to take my classes and carve out time to do them. BUT as a parent myself I think they are over burdened and over scheduled. I hope none my student's parents read MT

.
Now as an instructor, I hate to see my students take breaks, because the student faces different issues coming back and they more than likely won't. However I also see the need for them. I think the kids should have variety in their life experiences so I want them to take band, drama, to pursue swimming. MY daughter who is in my Modern Arnis program tends to miss a lot due to band, church, etc. etc. but I enjoy spending time with her, in fact I treasure it, so I keep the long view in mind. I want my daughter in the martial arts in her 20's 30's etc. etc., so I'm not worried about pushing her in her early teens. I do make her go to class with me, she does demos with me etc. etc. but I'm not worried about how many classes she's attending, nor am I setting the pace for rapid advancement either. We train sometimes outside of class so we both enjoy the time together.
But back to my students taking breaks, one thing I hear from parents, "we're going to take a break for X amount of time" (a sport season) is common, "then we will be back". The student wants to come back but all of the sudden they aren't up to their skill level when they dropped out; now doubt, insecurity, all start to creep in. Pretty soon they are making excuses to stay out and then they are lost and it is much harder to get them back. Sometimes I tell the parents (in fact more often than not), keep them in one class a week so they stay connected to the school, they remember their forms, their kicks etc. etc. I've had parents tell me "we will be back after this season is over" only to hold the kid out for 6 months or more, then the kids get behind their friends in class (rank wise) etc. etc. and it is even harder and more frustrating for the kids. So how long your daughter might want to take a break is anyone's guess. Maybe after her test you need a break from your (her) training schedule but not from the martial arts.
I do have the utmost respect for her teacher, but he just seems to get more and more paranoid about the government and how "they" are out to get everyone. He can believe whatever he wants to believe, I respect his rights in that manner, but when these ramblings start pervading into classes with young, impressionable youths, and start overshadowing the art that they are there to study, is where I have a problem.
You should tell him so, as well. Just because he is a higher rank he doesn't have the right, well he has the right, it's just bad business sense for him to do what he is doing, and you have the right to go somewhere else, where this doesn't take place. Your master is just a man like anyone else, he might be a great technician, great teacher and very skilled, but after being in the martial arts for 30 years there are plenty of good instructors out there in different arts. He's not the end all. Seriously I recommend you have a private conversation with him and explain your view point as a paying customer and as a parent not a student. If you go to him as a student he has the upper hand in a sense, but as a customer you do.
I viewed your profile and saw where you are a cho dan as well, is this correct? So are you taking classes with your daughter? If so that very well might be why she attends so many classes or doesn't want to quit. It's family time. Frankly if this is the case it would probably be fine where ever you went.
Good luck, and if you talk to the guy, or you leave the school, or you resolve the issue please let us know. I would and I believe the others as well would like to hear what happened.