YANBU - it sounds to be like you have 4 kids and one of them is a BIG BABY (not the cute rewarding kind either).
Clearly this pattern hasn't just started but has been going on for years. How have you lasted this long OP feeling this way? I would be hugely resentful if my DP acted this way & our relationship would be a mess.
Not only is your P opting out of parenting and electing to act like a selfish teenager, but when he is forced to contribute, he acts all passive/aggressively by undermining the kids bedtimes, routines etc. And I take it you cook AND clean up for the evening meal? FFS that is taking the piss big time in my book.
I agree with what many of the posters here have suggested. As for going out for a night and leaving him to it, I'd be making plans for an entire week.
Still I fear that this has been going on for years, and for effective proper change to occur is going to involve some serious and fundamental changes in your relationship.
I could not have sustained a relationship with someone who acted like this. Poor disinterested lazy father, and goodness knows how you manage to have sex with him - if I was treated this way by DP there is no way I'd be remotely attracted to him at all. What a turn off.
As for those suggesting its your job as a SAHM, well when does that end? So if you work outside of the home you can expect to come home, not parent, not contribute at all and expect your SAH partner to do everything all evening long too? Mugs game if you ask me and completely unnecessary. As a SAHM aren't you working all day too?
We both do the after work/meal/bedtime stuff - get DD off to bed, one of us cooks, the other washes up, and when that is done then we chill out, go on computer etc. By sharing if one of us wants to go out and not be there for the night, or is sick and needs time out etc it's no biggie for the other person to do it all - because we know the other person respects what we do and will do the same when necessary. It's how our partnership works.