I've never dealt with a filly like that. I've had my girl hands on as soon as she was born! However, my friend is boarding her wild mustang gelding at my house now. Just brought him over a few weeks ago. He's been wild for 8 years and domestic for 1 year. My friend got him for free from a lady that was terrified of him and never really worked with him too much. Once you've caught him he leads and such, but you can tell he is still afraid of that halter a little bit and still shies away (snorts, shakes, ect..) I've only really worked with him one day so far. School and stuff has been limiting me. When I got back to my dad's next week though I plan on working with him more.
That's good, I wouldn't trap her either. That might make it take longer to train her in the long run if she develops trust issues. However --once you are able to approach her nicely and she seems to trust you more. I wouldn't let her get away with that too much!
I would try possibly just hanging the (or a) halter by where you feed her. (As long as she's not going to ruin it by nibbling --I can't leave ANYTHING where my filly can reach it haha) That way she can see it and get used to it. At first I would just working with approaching her. If you get close to her and she looks at you interested then take a step back maybe. Let her know maybe that curiosity is a good thing and as soon as she is a little curious you're not going to rush up on her. Also, I'd work with approaching her then walking away (first without the halter). Then, once you can approach her without the halter start approaching her with the halter. I wouldn't put it on her the first time though, let her smell it and get used to it in your hand. That way, she won't expect to have something strapped onto her head each time she sees it. I've done this with my horses
-I let them loose to graze in my yard. At first, they realized that if they saw the halter in my hand it was time to make a run for it. Soo, I started going up to the with the halter all the time. Sometimes I'd put it on them then take it right back off. That way they don't associate the halter with being put away. Just a suggestion, I'm not a professional trainer by any means especially with scared horses. Keep us updated! Good luck!
Riding a horse is not a gentle hobby to be picked up and laid down like a game of solitaire. It is a grand passion. -Emerson