Honestly love, the best Christmas present you could give yourself, and your son, is to get this sad sack of shit out of your life
Wise words Anyfucker
And I think Quintessing has good points, too.
If his mother has "sold" her house to a mortgage company (Is it some form of equity release? I'm not very financially aware, I'm afraid) then I'm not sure how you could "buy" her share from her. They will be wanting their money on her death (not saying she's trying to scam you - she may not understand how things work either - and TBH I could be completely off the wall).
He is a very selfish man - he's putting his own "wants" before everybody's needs, including those of the sone he supposedly loves so much, and the mother he allegedly wants o look after. He is destroying his son's opportunity to be part of a family, and just moving in and out of his mother's home (and I'll bet she does all his cooking, washing eft) as it suits him.
He's trying to guilt you into feeling responsible for the breakdown in the relationship when it is his fault, he has undermined you financially and is living off you, he is full of self-pity and "poor little me" - whatever you, or anyone else does, he is going to be a selfish, manipulative tosser,and he isn't worth a light.
Your ex sounds a thoughtful man and definitely take him on his offer of help. It's wonderful that he still cares so much for our child and you that he is prepared to do that.
As you have paid the deposit and the rent, I can't see that there should be any problems about putting his belongings in a black liner and telling him to get them shifted. TBH I would be tempted to lock him out when he comes back from the party and tell him t goto his mother's. And not let him back.
You aren't responsible for him, you don't need to keep him, and you certainly don't need his spite eating away at your self-confidence. Take this as a lesson learned. it could have been worse - you might have married the bugger!