I do see your point.
Was he single when you met - or did he leave them for you? Is your response driven by guilt and anxiety? He's done it to her so he could do it to you?
Getting together with a man with a child means child and mother, a unit, will be in his and your lives probably forever in one way or another.
He is being present in his child's life, which is great, so it makes sense he's ensuring their home is comfortable. If he left them, guilt may be a factor that keeps him going back to help.
If you want to remain in this relationship you'll have to accept all that.
Giving him a meal in return for what could be expensive work otherwise seems reasonable.
But it could also mean she's considering taking him back.
Two domestic set ups must be very cosy and convenient for him. But you haven't yet reached the point when your space is shared and him just walking in feels like a presumption, and intrusive. Especially on top of your unease.
Telling him to go away? It seems that's the clearest thing you've said to him over all this, a specific statement of your feelings and wants, and he's listened.
So what you need to do is talk to him, use your words, tell him exactly how you feel.
And ask him the same thing.
Be careful - as we know, they can and do lie.