Then do yourself a favour and ditch him.
He's 30 and still behaving like a teenager. He's not going to change or suddenly decide to grow up. At 30 he is who he is, a fully formed adult (or man-child still controlled by his mummy, in this case!).
He's got one foot in your relationship at best and only one toe in DDs life. He's doing minimal parenting, doesn't want to live with you, but happily saves himself some housework and bills by staying at your place half the week, where he spends as much time as possible away from DD and hanging out with friends or doing hobbies. He's acting like someone who doesn't want a family at all. I suspect he's basically just around for the sex, isn't he.
Meanwhile you're wasting your youth on him, when you could instead be single, open to the possibility of meeting someone who actually does want to be all-in and be a family with you.
You're currently letting him cherry-pick the bits of a relationship and parenting that he likes best, whilst simultaneously he's avoiding all the day to day grunt-work and compromises and teamwork of living with a partner and raising a family.
The homes situation is bullshit excuses. It doesn't have to be your place or his, you can both look jointly for somewhere else that's more suitable!
He also doesn't need "his space" in the property. Women don't have their own space! It's just a home where everyone lives.
He's not going to be a lodger, the plan is he moves in to be a family member. The fact he's not looking at it like that but in terms of carving out a bit of space just for himself, separate from you and DD, speaks volumes as to his general attitude towards you. He sees you both as an option, an add-on to his life as opposed to people he shares a life with. You're a situation he wants to choose to opt in or out of even if living together, hence wanting "his own space". He's not seeing you and DD as people he's already committed to (or should be!) by the act of creating a child with you.