Serkeen, first of all, so sorry about dh's illness. Hope he is ok now. You've been through a lot, lately, and for that reason alone, imo, dil should cut you some slack.
That being said, I hate when someone cancels last minute! This was especially true when I was a young mum and someone backed out of babysitting (yes, it happened to me a couple of times). It would change my whole plan for the day. Sure, sometimes there's an emergency or a serious illness and I understand that. But just for "feeling stressed?" I'm sorry but I would have been upset by that, too.
I would have accepted it though. No one "owes" a parent their babysitting services, unless they've being paid for them. And, as I said above, I would have cut you some slack due to all you've been through lately.
Obviously, dil didn't really "need" a babysitter, as she was able to manage on her own. She just "wanted" one to make things easier. Nothing wrong with that, but no harm done either that she had to take gs with her.
In the future, I'd say, "I'm sick" if I had to back out of babysitting. Or just make sure I only agreed to do it during a week where I wasn't going to have a lot of stress. Or just make up my mind to go through with watching gs unless I have a fever, etc. Just my thoughts.