We called our school Ving Tsun Arizona (you can still see the old web address in my signature below). About a year ago, I finally let that go. Now I just coach a couple of guys semi-privately, strictly word of mouth.From how you explain it, it sounds as if you were a class and you didn't advertise yourself as a school. If you advertised as a school then what was the name of your Wing Chun School?
Anyway, we never had any conflict with the boxing classes. Barely saw them. We just used the studio space for an hour and a half, three nights a week, plus Saturday Wing Chun and Escrima classes at a nearby park ...and a few other venues over about a dozen years.
If you were really trying to make your living off teaching full time, I can see how you could have problems. But that was never my objective.