Bit worrying for her if this relationship goes tits up. She's bankrupt & seemingly has no assets to her name. Sure he will have to pay maintenance for the children but she will find herself living a far more modest lifestlye though the children won't suffer & the private school fees paid etc. Not beng married really does go against you in these situations.
He doesn't want her name on the house, won't pay up to prevent her being declared bankrupt - how much does he truly love & trust his partner? Yet despite all these signs of not commitment he is happy to have children with her. If a partner bears you children you really should be happy to share everything such as the house etc. (and yes debts/tax bills) even if you earn far more money, that's what a true partnership is.