Ok OP I would sit him down and talk through how things are going to work out if he lives with you all.
Both of you with both of your expectations.
So if he wants you to so all cooking, cleaning and laundry he has to contribute financially. If you are losing money he has to make that up plus some to go towards bills, food, fun for crying out loud.
You should agree that future discussions or changes should be talked over openly, honestly like adults. If in future, IF, but needs to be spoken about, you split up he leaves this is your house for the kids.
You can support him in his work helping make his home life happy and as stress free as possible he can help you with the kids, being a dad basically and with money.
You can't start out on family life without establishing reasonable expectations of each other. You should have done this before he moved back. But do it now, soon.
If you can't come to an agreement then he should move back to parents and pay you child maintenance.
You guys need to work together to have a happy family life. If it's this conflicting now it is likely to just get worse.
Hope you sort it out.