AITA for refusing to split custody?

I have fifty/fifty custody of three of my kids: Joe (12), Sue (10) and Tim (9). I also have two other children. We have always alternated custody on Mondays. I drop the kids off at school Monday morning, she picks them up Monday afternoon, and next Monday she drops them and I pick them up.

Lately Joe and Tim have been fighting a lot. I've been doing my best to handle it at home, but their mother says she can't deal with it anymore at her end. She wants to split the custody so that half the weeks I have Joe and she has Sue and Tim, and half the weeks she has Joe and I have Sue and Tim. I would have to agree to this for her to change the custody order. I am against this idea for several reasons.

First, this is unfair to Sue. She would never see her older brother anymore. The two of them get along perfectly well. Two, this is a bad lesson for the boys. They need to learn conflict resolution. Three, this is hugely inconvenient for me, because it would mess up the babysitting schedule, and I always schedule personal medical appointments and overtime at work on the weeks I don't have the kids, which would no longer exist. Four, I think she's being really lazy. I always try to run interference with the boys, and when I drop them off at school, they are usually at least at a begrudging truce. Whenever I pick them up, they are in the middle of a fight, and Sue told me their mom does nothing about the fighting, mostly ignoring it.

I don't think I should inconvenience everyone to make life easier for my ex-wife, who doesn't want to do her job as a parent. However, she insists I'm being a huge asshole and putting my needs over those of the boys. I think she's being a pot accusing a kettle, but which of us is the ass.