Just to flip it for a moment, that clearly means he owns 30 percent, even if you decided to buy him out maybe with help from mum. His 30 percent will leave him enough for a deposit and an enormous mortgage with currently extortionate interest rates.
I haven't read your other threads, thank goodness you protected your 70% though, but from reading here, he drinks, does drugs. I just wonder how attractive he'll be when he has no money to spend on her. When he'll have to contribute to the upbringing of his child, when he'll have to pay 100% of his own bills on his new place.
This idiot can't see how much he is giving up.
I'd take control of this situation, right now he thinks he's coming home after seeing his other woman, whatever shite he's telling her we don't know.
He has her, he has his home, he has daily contact with his child and he has you heartbroken, naturally. Get control, see a solicitor, see if you can legally get him out, see if you can buy him out. get his ass out of the home so you don't have to see him. That would be torture for me.
He's not being fair to your child either, putting his mum through that, selfish man.
Take control, get legal advice on how to get him out, buy him out, but get him out of that spare room for your own sanity.