Your post isn't clear - are you saying that food, rent and bills are paid for out of your joint UC and your wages?
He then spends half his PIP on his phone and a car? Do you mean the actual car payment, tax, insurance etc? Is this a joint car you both make use of? Eg, you go food shopping in it, go to work in it, use it for trips?
This all seems reasonable so far.
You say he then has £350 left which he spends on his hobby. You also have money left, but you spend this on meals out, both of your clothes, haircuts, fuel...general joint expenses. When you say "you" have money left, is this left from your joint UC/wages? Or just your wages?
If you are bringing more money into the household each month than him, most people would find it reasonable for you to contribute more to joint expenses. However (and it's tough to say exactly as you don't state what you earn or how much you have left each month) if you're receiving benefits, I think it's safe to assume that £350 would actually make quite a difference to your monthly budget.
PIP is intended to be spent on things that will make the claimant's life easier - his car to get around would be a good example, his phone to communicate with the outside world etc.
Technically though, it can be spent on anything that improves his quality of life/ease of living. You haven't said what your partner's disability is, but if it's a mental health issue, his hobby might be his saving grace. If he's restricted physically, his hobby might be a connection with the outside world. Consider that it might be the only thing giving him a sense of agency or purpose, and the effect removing it would have on him.
However, if it's solely your money (outside of joint UC) that's going on clothes, fuel, meals out etc that you're both benefitting from, you will need to be clear to him that he needs to contribute more.
My best advice is to make a spreadsheet or a simple list of your income and outgoings. Show him what the joint UC covers, show him how much of your 'own' money is covering joint things vs what he pays for the car.
If you think he's refusing to chip in more for genuinely selfish reasons, stop paying for his meals out, clothes and haircuts. You may also want to consider what you're actually getting out of the relationship.