AITA?

Ladies, maybe I just need some words of affirmation or maybe I truly need to look at the situation from a different angle and maybe I am the one in the wrong.

A little back story, I’m a nurse who works 3 days a week - 12 hour shifts (7a-7:30p). My fiancé works, but has weekends off. Anyways, we got into an argument late last night and he said something that keeps replaying over and over in my head. Our argument was over me saying that I needed to go to sleep and that he can watch our son until he finally decides to go to sleep since he’s the reason his sleep schedule is messed up. He went on by stating how he only views me as a part time parent, how I didn’t do anything for our son once I got home from work last night besides change a few diapers, try to feed him dinner and change him into his pajamas. Which is somewhat true, but I also played with him for about 30 minutes as well.

Our son is 18 months old and for the past month or two, I have tried my hardest to get his sleep schedule back to normal which typically happens when I’m home but once I go to work, it’s back to being messed up due to his dad allowing him to take late naps (anything after 3-4pm is a late nap for him since he naps for about 2-3 hours). For example, Friday, our son woke up at 9:45am and didn’t want to take a nap all day, no matter how hard I tried so I kept him up and he went down at 8:30pm and slept until 9am yesterday morning. I texted my fiancé while I was at work around 6pm yesterday to see what they were doing and he stated he was trying to get our son down for a nap - I told him no, it’s way too late for him to take a nap and to keep him up for another couple of hours. Anyways, he didn’t listen and put him down for a nap. I got home at 7:45pm and they both were sleeping on the couch. I was able to shower, fold 2 loads of laundry, pack my lunch for work today and put away dishes before they woke up which was closer to 8:30pm at this point. I finish getting dinner ready, cleaned the kitchen, got our son into pajamas, played with him for a little and then by 12am, I was starting to dose off and he was still bright eyed and wanting to play. I told my fiancé, he needs to take him so I can get some sleep since I had to get up in a few hours for work. That’s when he began to say that I’m a part time parent and he was with him all day today and needed at least an hour break, How I ruin his weekends when he’s off and I have to work, etc. He walked out the room, went downstairs for his “me time”. So, I had our son and then our son finally went to bed at 1-1:30am.

Am I an asshole for wanting to put our son off on him? I mean I told him not to let him take that nap. I just idk, I struggle so bad with mom guilt and when I’m being told that I’m only a part time parent due to my work schedule, it stings ya know? because no, I didn’t get to spend as much time with our son yesterday when I got off because they were literally sleeping but it wasn’t like I just got home and went straight to sleep. I did things around the house and did what I could.