Are you asking for too much? No, you don't! Who, except yourself, has the right to decide what is too much for you? You feel bad and want it to change, you feel like you can't handle the situation. Of course, you're not asking for too much, if you see things that way!
You probably feel like you have three options: If things don't change, you will go on suffering, he could change his behavior or you could leave. I would like to offer you a different view, a forth option: You could also choose to stop suffering!
That might seem a little provoking, but let me explain: We feel like we need other people to meet our needs and expectations to feel happy in a relationship. We feel like we need to feel loved, needed, wanted, otherwise we feel bad. I shared that view for quite a long time in my life, so I'm quite familiar with it. I've learnt for myself though that it's not anyone else who makes me feel bad but myself. If I choose not to feel bad any longer, it doesn't matter how much time my partner spends with me or someone else, what he does with me or others, how he treats me (as long as he's not forcing me to stay with him or keeping me from doing things I like). I don't need him to make me happy, I can make myself happy! Instead of sitting at home, being grumpy that he sees the other woman, I can go out and meet other people myself. Or I can enjoy my alone time. And then I'm less grumpy when he comes home, I have something to talk about. I don't feel needy but in a position where I can give and share my happiness.
You say you can't deal with the situation. I say, you FEEL like you can't deal with the situation. But I believe that you can learn to deal with it. It is possible, and it requires no skills that anyone with a working brain doesn't have. Learning to deal with it would give you more freedom of choice, and the ability to deal with a lot more situations in your life.
So instead of leaving the situation or asking him to change anything about his behavior, I would take the chance and work on my own feelings. It's a great opportunity!
But this is just my opinion. I know many people have a different one. You go choose your own.
About the car, I would suggest you to be brutally honest with yourself: Why do you want to give it to him? I wouldn't do it if you feel like you could buy him with it, or tie him to you. That probably won't work very well, I guess, or at least not make you happy in the long run. Give it to him if you really just want to give. Also check if you can really afford it. Money is something we really need to survive and feel good, so we should make sure we always have enough of it. There's no point in him having a car if it makes your life worse financially.