This. Don't do it, OP.
I know it seems unfair, but when there isn't shedloads of money to go round, both parties have to be housed according to need, not according to want.
I'm sorry to say that it doesn't matter that your son is young for his age; he's an adult. It doesn't matter that your daughter likes the area you live in; what matters is that you and her father are both able to house her adequately. Unfortunately this often means you both end up with less nice houses - because the budget simply isn't there for it.
It's also unfortunate and feels unfair that you bought the house cheaply from your family - but marriage is a legal contract giving both parties financial rights, and people should be aware of this when they enter into it.
In the case of your daughter liking the area you live in (which is presumably also where she goes to school): the expectation would be that you could either buy a smaller house in that area, or a bigger house in a cheaper area. You can't buy a big house in your preferred area, sad as it is.
If I were you - and I know you have had legal advice - I would put the house on the market because pretty certainly you're not going to be able to stay there. You will need to give him his share of the equity, which is likely to be around 50% given the ages of your children (it would be hard for anyone to claim that a 13 yr old needs a SAHP who, therefore, needs more equity to buy a bigger house).
If he does take it to court - which I would strongly advise him to do, if you refuse to sell - then he will win. Save yourself the anguish and the expense.