[MrEricka]

If I can throw my two cents in here.

Good suggestion on the movies, however... most trans movies show drag queens. As explained by Noxeema;

Noxeema Jackson: When a straight man puts on a dress and gets his sexual kicks, he is a transvestite. When a man is a woman trapped in a man's body and has a little operation he is a Transsexual.
Noxeema Jackson: When a gay man has way too much fashion sense for one gender he is a drag queen.

Since mom is homophobic, this could be a poor choice of a first movie to watch.

You want to educate, but not enforce the LGBTQ aspect. Take a look through the list below and maybe preview the movie first to see if it steers away from mentioning homo/bi sexuality. After a one or two "clean" movies THEN move on to To Wong Foo or my favorite, Kinky Boots.

Tell mom you want to have a movie night once a week. Mix it up and slowly work them in. Have a minor discussion about the movies afterwards to get her feelings towards the characters. After a few weeks she may see the situation in a different light.

TLDR;

Take it slow

http://en.wikipedia.org/wiki/Cross-dressing_in_film_and_television