marieneedsaholiday I am a lurker but I must de lurk to ask are they his kids or just your kids?
If they not his kids, why is he disciplining your kids? Unless you really trust him, IMHO, he should not be in charge of the kids or looking after them when you are not there. If you are there it is not his place to discipline them. Especially if he is heavy handed (metaphorically speaking or in any other way).
He sounds like he is gaslighting you about your mental health, which makes him monummentally untrustworthy.
Why is he not getting up for work? Does he work? Is he living from your income or his own private income? Why do you need to get a better job or house? Sorry so many questions but if he is your boyfriend it's none of his fucking business what job you gave or house you own.
Is this a partnership? If this is a partnership, what does he bring to the table?
He sounds fickle (might marry you, might not), lazy (might not work), uncaring about your feelings, pressurising you, (is he living withyou rent free?) and unaware that he is 'over disciplining' your children.
What does he bring to the relationship? In your shoes I would re-evaluate whether this is someone you want around you and the kids.
Aspergers or not he sounds like one giant pain in the arse!