I discussed it a bit more with him. A one clarifications first: We are happy with the appointment that is made now. DH just wasn't happy with how much effort it took to come to an appointment.
I think he is directing his bitterness about his sister to his parents. Like I said earlier, he doesn't get along with SIL well. To be honest, from my POV as well, she indeed isn't a very easy person (always angry, quick to snap at anyone) and entitled when it comes to the babysitting. The few times the parents in law went on vacation and announced in months in advance, she had been acting up about it. That contributes to the feeling of DH that his sister walks over their parents (their spines not always being very strong) and claiming their time and attention.
But! it's not like it changes the facts. The parents in law agreed to watch over the child, and that's what they do. And I agree that one week in advance is still a small amount of time. Plus, whether the SIL is being difficult or not, this arrangement is something his parents chose to do themselves. No one pointed a gun at them. DH has been a bit dark about this whole issue and spouting lines such as 'well, we'd better not land into the hospital on a saturday then' --> which is very uncharitable towards his parents, as they have helped us out in the past and I believe that they would do so again in the future if an emergency would come up.
Geez, it is soe difficult to untangle conflicts and issues when not directly involved. In case anyone wonders, I'm not putting myself in the middle, but I'm just trying to help my husband to come to terms with this and give him other views on this issue, hoping it will help him.
ps: the reason I gave too much background is because I didn't know anymore either what was relevant or not. Maybe it's the 'she made this choice to be a single parent and lets others pay the 'price' for it' vibe I got from DH. But as noted above - the help she gets was a deal that all involved people agreed with.