Edit...
After reading Leigh R's response, I see there is more to this. And after reading your other post, I have to agree with her. You are being petty. You did initially say you paid her for the hrs, now you are changing your statement. That's about as confusing as leaving the money for them, telling them to use it, but not really wanting them to, and then when they do you get offended. Did he grab the money as he stormed out of your house because of his broken laptop? Or was it gone before that? Did you even notice whether the money was there or not when you arrived home? None of that really matters, I guess.
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Personally I wouldn't have taken it, especially if I had expressed being hurt that you never asked me to sit for you. On the flip side, my husband probably would have taken it. He feels that if it's offered then you should just accept, so as not to offend anyone. His logic took me by surprise because he is the most generous person I have ever met. He'll pay for dinner when we go out in a group, which I always disagree with. I also think that since you mentioned it was there if they decided to order something, should have also been a clear sign that it was there for food. Maybe they went to Olive Garden or something. Lol
I kind of agree with Kim O. In the sense that you didn't really intend for them to use it, but then you laid it out for their use, can be confusing, especially if they think like my husband. However, she is your SIL, and knowing your financial situation, I think she should have just left it there, with a thank you note, for the gesture.
She may have driven far to watch the baby, but it was something she wanted to do, and if she couldn't afford to do it, then she should have kindly declined and said that she would be more than happy to, the next time she was in town.
I'm not sure if you're asking, just to ask, or if you're asking with the intent to say something if you so feel justified by the responses, and I know you didn't say you had any intention to say anything, but just in case, I wouldn't say anything to her or anyone else that could repeat your displeasure in the scenario. I would just make a mental note of how to ask her to sit for you from here on out. Or just wait until she offers.
I think you might be a lot like me, where you just ask to see if others perceived the situation the same as you did.
To answer your question though, no, I don't think it's petty. I think this is a great question and it also makes you more aware of how to handle your sitters from here on out. Family or not. :0)