I think he’s planning on cheating on me

I am a mom of 3. I have a 3 year old, a 2 month old and I also have a 7 year old. Between all 3 of my kids, my younger children definitely keep me on my feet And they exhaust me. I’m always tired and since my boyfriend works literally 12 hour shifts (yes he’s their father) by the time he gets home I just wanna give him the kids and sleep. For the past few months he’s been complaining that we haven’t had sex in months and I don’t say anything. He says I only initiate sex once in a while And that every time he asks I just roll over and fall asleep.

Today I went to a family function and he asked me if he could get a girlfriend and asked me to be open to the idea. I got mad and told him no. But it’s not the first time he’s asked me this. It’s the 3rd time this year. He also says that he’d rather pay someone else’s bills because he doesn’t see a point in him paying every bill in our home for the past 2 years and anytime he asks for sex he’s rejected. It’s been about 6 months since we did anything. But honestly I’m tired and if he lives here he should help out with no complaints.

He also complained that every time he tries to get some sleep, that I take the baby with me for short periods of time like to cook and then I hand him the baby while he’s trying to sleep. He said he has no problem taking care of the baby and that he spends lots of time with him but that he can’t “catch a break” between bills, no sex, and kids. I understand he’s tired from work but that’s part of being a father and I don’t understand why he keeps bringing up sex. It’s like he wants to make a complaint just so he can have a reason to cheat.