sbwilson has a really good point: your dad may be undiagnosed AS, which will make him accepting your diagnosis all the more difficult. After all, the way you are is "normal" to him and his parents, and accepting that it is not would require a huge upset in every assumption they've made throughout their lives. He is going to rebel against that every step of the way.
Whether or not that is true, I think your dad loves you, but he is clueless. His whole world just collapsed, just as yours did (I am so, SO sorry), and all while having a teenager, which, shoot, no parent ever understands. Its hardwired for teens and parents to fail to understand each other; its a necessary step in the teen becoming their own person; but throw that on top of all each of you has been through and, well, it must be insanely difficult.
But understanding why the situation is as it is is only going to get you so far.
I would suggest you start by asking him if he is willing to do his own research on Aspergers. Find him some articles or books; point him to this forum. Let him start immersing himself in it in his own way and in his own time. Tell him that you accept he doesn't buy into the diagnosis, but since you don't know how to be the son he seems to need at the moment, you think a first step might be trying to get him to understand what the professionals see or believe they see.
The girlfriend. Sigh. She sounds selfish to me. She wants your dad but not an almost grown son, and she is going to try to drive a wedge in between you because that gets her what she wants. Don't let her. Don't play the game. Don't engage. Move into robot mode when she is around. Be the perfect child - yes ma'am, no ma'am, I'll be in my room doing my homework. Don't give her the opportunity to make you look bad. I know that will be so, SO hard; she has tools that you don't, but please try.
Just don't give up on your dad. Or on yourself. You are both emotionally scarred right now, and in need of something that neither of you is capable of supplying at the moment. Your dad thinks he has found an answer in this woman; he hasn't, but he'll have to figure that out on his own.
Don't be afraid of being a burden to your friend's mom; if I was that mom, I would want to be there for you; it wouldn't be a burden; it would be the only gift I could give someone I cared about in a difficult situaiton. I really care about my son's friends; if I could be a help to them, I would in a heartbeat. It's part of the mom instinct; something we need to do. Accept it, use it. Be grateful.
Take care.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).