I'm gonna offer some advice here that might not be the first thing that comes to mind for a lot of people, and a lot might disagree with, but if it doesn't sit right then ignore me.
This is probably hard for your mother to deal with. I can't claim to know the situation exactly (or very much at all), but it's the kind of thing that can be very difficult to come to terms with - there are a number of things she could feel, a lot of them quite possibly more negative about herself than you. It's probably worth trying to make this as easy for her as you can. (That's the advice a lot of people might disagree with.) The easy reaction is to say "Well, it's her fault for being so close-minded and it's not my fault I'm the person I am", and sure that's actually perfectly true. And I'm not accusing you of feeling this way.
It's just that it's not conducive to good dialogue and a healthy atmosphere. She might be hoping that you'll somehow 'prove yourself' by paying for gas even when she offers to do it for you. She may very well be accidentally (or not accidentally, but I'm inclined to give the benefit of the doubt) screwing you over with a no-win situation. There are a lot of options.
Have you tried sitting down and having a calm, cool discussion where you discuss why she doesn't like you being trans and what you can do to mitigate it? You might have, in which case I apologise. And to be perfectly, I don't mean you need to let her stuff you back in the closet, but if there's something that she'd be happier that you do or somesuch, see if you can discuss it and come to an agreement. Mostly because so far I don't get a totally insane vibe from what you've posted.
If it happens that you need advice responding to any religious objections she may have, you're welcome to ask me. Or OW, probably, he's pretty clued up as well.
If I've accidentally been insulting or anything, I'm terribly sorry. I think I have your best interests at heart, which is hopefully what counts.