I would stop trying to talk to them about it and do everything you can to get out on your own as soon as possible. Meaning - sit tight and do what you need to leave ASAP - get a job if you don't have one all ready and save money, etc. I have no idea how possible that is for you, but you have to make it work. Time to move on from your family - for your health, safety, and quality of life.
You can't argue or convert their level of ignorance and hatred - not at the same time you are battling them to accept you simultaneously (in their minds) as having a girlfriend and being transgender. The most open minded parents have trouble with this - it is 10000000x worse with parents who believe what yours do.
If you drop it completely (in front of them only of course) and just act like you're moving out because you're an adult and want your own space, you might even get to keep your car. It will probably be a bit of time before you can move out safely, right? That time will be a buffer to dissipate the threats of him reporting it stolen. Maybe. Tread carefully with this one, of course. Don't let that car be your leash.
When they talk to you about any of it, just be civil and smile and say you are putting it on hold for awhile while you sort yourself out. Which is completely true. You are putting it on hold with them, not with yourself.
They want you to go see a gender therapist that will talk you out of it, not work out your feelings.
Leaving home doesn't mean abandoning your Mother. It means giving yourself some space from them, and them space from you. Eventually, time will help you work out these problems with them. But honestly - that is not going to happen while you live with them. It will take years most likely.
You need a backup plan at all times to leave the instant any violence or threats of violence appears - like other people have said, get bus passes, stash some cash - keep a bag ready.
TLDR - you have to stop talking about this with them or the stress levels in your home will eat you up and ruin your life as long as you live there. Act like you are putting it on hold. Be as nice as possible and do not create friction. Pander to them, and then leave ASAP.