M.G.
I'm not divorced, but I've never had an issue with bedtimes because as others have mentioned, I start winding down early. We have done this since the start. I used to have my kids bathed (as something to do with them) early, and ready for bed, then they could play quietly. But I get the stuff that had to be done - over with ahead of time. It set the mood that we were winding down, and it's much easier to get a child to brush teeth if they're not tired and cranky.
I also read to them, and then allowed them to read a bit (once they got to a certain age) so bedtime was fun, not some dreaded time.
The people I know who struggle don't have a pleasant routine. The parents are tired and cranky and it's just stressful. I know I get more and more tired as night wears on, that's why getting the work done early, means you can veg with the kids later. He could tell the kids if you get ready for bed, we can watch a show together before bed, and if they fuss - then no show, right to bed. Whatever works.
I don't know about feeling bad for being impatient. We're all impatient at times. Some nights my kids are allowed to read in bed, mom's too tired. My kids adapt. No point in feeling bad about it. But I don't chase my kids. There are consequences if they give me grief. So he has to get used to that I'm guessing.