Oh Dear. His insistence on paying for a house on a Mortgage which isn't occupied makes absolutely no sense. I believe you when you say he is a good dad and not a bad person and you clearly love him.
It sounds to me as if there is something more going on in his head than 'wanting to leave something for his son/stepson' - something maybe he isn't aware of himself, because to most people what he is doing with regard to his house is crazy.
Taking the Mortgage payments out of it, for the moment, can I suggest that you start off by looking at the divsion of financial burden between you and rejigging it. You say he earns about half what you do, so I would suggest that you draw up a budget by looking at all the regular expenditure you as a couple incur ( including your rent Council tax etc but not his mortgage) and also including what he pays in child support and work out what the budget for all that expenditure equates to per month, and you agree to pay 2/3 and he agrees to pay 1/3 of all of them. )You can adjust the percentages depending on the actual difference between your income). You can include a holiday budget in that, or not, and also a clothes budget, or not. Lots of different ways to deal with it, but your current arrangement, while I can see it made sense in the beginning needs to change for both your sakes.
This is only fair and if he's not prepared to do that then I do think he is maybe not as committed to you as you are to him.
Once that has been worked out, you will be able to see more clearly how much 'free money each of you has to spend as you each see fit. That may very well show him that he can't afford the Mortgage.
Even if it doesn't let him see that, and even if he now decides to sell the house It seems to me this would be a good thing to do, regardless as it would be fairer and less likely to cause you resentment now or in the future. At the moment he isn't paying his fair share which is why you are resentful and I would be too. A fair share does not need to be 50% each as I said above but a fair share of expenditure vs income - like 66% vs 33%.
At the moment, your partner is making it so that you cannot actually afford the things you did before he moved in with you - when in fact a second income ought to help a bit, so something is seriously wrong financially - and maybe not just the Mortgage payments
Good Luck