Am I in the wrong?

A little back story. Me and my SO have been together for 2 years. We have an 11 month old baby girl who I have been exclusively breastfeeding. I have 4 year old twins from a previous relationship and a stay at home mom.

Me and my SO have been arguing a lot lately. He tells me the house is my job and he doesn’t have to do anything around the house.

So I take care of the kids by myself EVEN WHEN HES HOME. Take care of the house by myself even when he’s off. He sits around and either watches tv or plays a game while I tend to the kids and house.

I’m touched out and overall tired. He constantly asks to have sex and honestly I’m not feeling it at all.

He told me if I loved him I would have sex with him because and I quote “we all do things we don’t want to do.” I told him I’d never do that if I didn’t want to. And he keeps guilt tripping me say he pays for everything and it’s the least I could do and that I don’t love him enough.

Am I in the wrong? Should I just do it to shut him up? What do I do?