OK, not so much "influenced." BUt because the Jidokwan joined in the 60's, GM Hwang included several kata not in his own syllabus in the Soo Bahk Do Dae Gam, and GM Yun later left because Hwang wuld not share leadership, infuriating many Jidokwan members, since technically, GM Yun outranked Hwang, as Yun came back to Korea in the late 40's a 4th Dan licenced Shihan in Shudokan(5th Dan being the highest rank in Kanken Toyama's style), while GM Hwang had about 2 yrs max with GM Yang Kuk Jin in China, and had a green belt from the Chung Do Kwan http://en.wikipedia.org/wiki/Kwans, and learned from books. Not that that is bad, but Yun had more formal training.
I was curious about the comments you made. So I have once again spoken with members of both the Moo Duk Kwan and the Ji Do Kwan. Some of the Moo Duk Kwan members I spoke to were instructors at that time, and basically this is what I was told.
The Ji Do Kwan never joined the Moo Duk Kwan. Hwang Kee started the Korean Soo Bahk Do Association in 1960 or 1961. Yun Kwei Byong and the Ji Do Kwan initially joined the Korean Soo Bahk Do Association. According to the instructors that I spoke to, the Ji Do Kwan members did not leave due to the Yun Kwei Byong wanting to be President of the Korean Soo Bahk Do Association. This is due to the fact that Hwang Kee was already elected President of the Korean Soo Bahk Do Association. At the same time the Korean Athletic Association was pushed towards governing the martial arts in Korea. Keep in mind that the Korean Athletic Association went through a couple of name changes before settling on their current name of the Korean Tae Kwon Do Association. Both associations were clearly going to be rivals. As a result the Korean government stepped into the fray officially in 1961. The Korean government only recognized black belts that were certified by the Korean Athletic Association or as it is now known the Korean Tae Kwon Do Association. This action caused many martial artists to join the Korean Tae Kwon Do Association including the Ji Do Kwan members. There was some debate as to whether Yun Kwei Byong joined the Tae Kwon Do movement and when he actaully created the Korean Karetedo Association. I cannot say for sure since my sources were not sure of this point. Either way, the fractioning was not due to the what you have alleged.
Also, the forms were not given to Hwang Kee from Yun Kwei Byong according to the instructors I spoke to. The instructors all told me the same source. But I cannot reveal that as of yet, since I am working on something I hope to have published in the future.
Best of luck to you.