You're being a bit contradictory and very dog-in-the-manger!
You feel threatened by his comfortable domestic intimacy with his ex, as he helps her improve the home in which she is raising his child. You also dislike his presumption of domesticity with you, just letting himself in and helping himself to a cup of tea.
You don't want that from him, but he can't have it with anyone else either?!
It's not logical, so something else is going on here, your insecurities, or maybe a gut feeling that this just isn't right for you.
What is your darkest imagining? That he screwed her (in front of their child, while fitting a kitchen and laying a floor) then swaggered into your house fresh from his conquest?
He shares a child with his ex, they are always going to be connected. However, a shared child is a strong motivator. If they wanted to be together, if their relationship worked at all, they still would be. It doesn't.
It's still best when separated co-parents are constructive, amicable, genuinely caring. He needs to be with someone who supports that.
Put it this way. How would you want him to treat you, when you are separated from him, and raising his child?