I'm 29 and I'd have some pretty sarcastic things to say in response to I need to try a guy...but you're 16 so there's even more pressure on you to act mature than there is on me, so I won't share my snarky comments (and being snarky--as tempting and understandable as it would be--isn't going to help you).
Generally speaking, kids find it easier to get along with their parents and get their way on things if they demonstrate a willingness to help around the house, taking an interest in their parents lives, getting good grades and staying out of trouble, stay polite, and possibly even getting some income.
The Truth About Jane looks like a good movie:
http://www.afterellen.com/archive/ellen/...tjane.html
I have no idea what your family dynamics are like and how much like an adult or kid you're treated like so I can't really make suggestions. If she's into making deals then maybe you could deal that you'll date a boy if she watches the movie.
That said...
How fair is it to a boy that you'll date him if you know nothing will come of it?
If she sets you up with a boy through family or friend then your ultimately rejecting the boy can possibly damage your mother's relationship with whomever she arranged to set the boy up with you which can have negative results for both of you as well as getting you both to resent each other.
If you must go this route perhaps it's better if you "cheat" and arrange to date a boy who KNOWS you're a lesbian (and isn't stupid enough to think he can change you) so you can hopefully satisfy your mom (assuming this is possible) while not hurting anyone in the process. Obviously, if you're not friends with any boys who know you're gay then this can be another problem...
Hopefully, while your sexuality is not a phase her denial is. Even fairly open minded parents can take awhile to get used to the idea that their own child is gay, and their not wanting to accept this may even be from a desire to not see you hurt by a world that can be cruel to those who are different (especially one filled with religions that condemn homosexuality).
And I don't know if it helps with the clothes, but if she's confusing orientation with gender roles then maybe you could mention the existence of femmes and lipstick lesbians (either humorously or matter of factly, not sarcastically). But it could be she sees that as a different issue.
Good luck. And don't forget--it gets better. Don't believe anyone who tells you these are the best years of your life.