I saw your thread title and wondered if my sister wrote this. But she doesn't have kids.
She feels the same way you do. Adding to her burden is that of the 3 of us, she is the favorite. He doesn't want to hear from the other 2. My brother and I have long gotten past that
She sucks it up and does it. Our dad is looking for the connection to our mother. She most resembles her and her mannerisms. My dad lives in my basement and checking on him at night is not good enough. My dad also is scared of dying and wants to know that someone will notice if he dies.
I wish I had better advise for you. She draws a boundary when she's on vacation and tells him she won't be calling. She has told me that she tries to do it when she's walking the dog in the evening. She mentioned that she says a lot of uh huh, hmmm, that's good---in other words she's not really listening. Because lets be honest, in 24 hours nothing notable has occurred. I handle all of the dr appts so if there is something medically wrong I let my siblings know.
Can you call him and not involve the kids? Sorry to phrase it like this but can it be just one more thing that has to get done as part of the kids bedtime routine. Get the kids settled down and then make the call? Let him know that the kids have gone to bed. And as horrible as this sounds she does say it can't go on for more than a few more years.....