I have come to believe that I will have to intervene whenever my x does something jerkish with regards to the kids, myself.

Recent example: S14 forgot his sneakers at his father's house, so he called him and asked if he could drop them off on the way to work. His father balked; had to leave for work early, was going a different way, etc. (he can drive right by our house). S told him he could even throw them out of the moving car rather than stopping - S would collect them from the driveway. He needed his sneakers in the morning so he could participate in PE.
X still said no - "Why is it always me that has to do it? Why can't your mother come and pick them up?" It was 9 at night, and X is 15 min drive from my house, so it would take me 1/2 hour, as I am trying to get them settled for bed...
S just looked at me.

I finally said, "S, just say goodnight and don't worry about it. We will get up early tomorrow and I will drive you to the other house for your shoes, then bring you to school, then bring D10 to school, then get to work. D10 will just have to get ready early with us and come along. You need the shoes."

Stupid. But I don't want my kids in the middle of him being an a$$hole. And believe me, S realized that his father was being an a$$hole. I don't even try to figure out why he does some of the things he does - I just do the best I can for my kids.
Maybe it is a twisted way to try to "instill responsibility" in the kids to remember their stuff? Well, it isn't their fault that they have to bounce between two houses - it's not normal! So, things are going to happen and be forgotten sometimes, and the adults have to behave like adults and take care of things.