Figuring out schedules with new baby

I work full time at Walmart & my fiancé works a part time job but my mom is his supervisor so he has a super laid back job. She understands his situation so he gets days off when needed, even gets to go in later (I know that’s not fair to the other employees). He literally only works 4 hours mon-fri but like I said he gets there later than usual so sometimes only 2 hours & he’s off on weekends. He’s mostly at home with the baby, our baby is 4 months. I know

It’s hard being at home all of the time with the baby but all he does is nag about it all day, it’s getting so bad to the point that I want to quit my job but I’m our main source of income. He claims he’ll get another job. Me & my babies insurance provider is through my job, my job is even paying for me to go to school online so if I did quit I would be giving up a lot. I really like having my own money but I’m tired of hearing him complain. Any advice?