Some other things to try in the future--if you don't want to outright say no, could you deflect with, "Let me check my schedule and I'll get back to you"? Then the next day you tell them, in a regretful tone, that you can't do it during their chosen vacation times because you're doing a special project at work or going out of town yourself or hosting a guest or something. Of course, if they check with your schedule first and then plan their vacation, that wouldn't work, unless you can plausibly say something like, "Ooh, this summer isn't good for me," and stick to it.
Or, think about what would make things better if you did house- and pet-sit, and how much work you were willing to do for that. For example, you said the dogs weren't leash-trained--do your parents have something against it, or do they just not want to bother doing it themselves? If the latter, would it be feasible for you to train the dogs, or arrange for them to be trained? Would that help your situation substantially? Or, when I was growing up, our cat had its own room with its bed, food/water, and litterbox, which was separated from our bedrooms. We put the cat in there at night and it didn't bother us, get into anything, etc.. Could you try that with your parents' cats, maybe putting them in the laundry room or downstairs bathroom for the night with everything they need, so they won't wake you up?
Personally I think you should turn them down flat next time, but what works for me in theory may not work for you in practice, so I think you should focus on being proactive in ways that you feel comfortable with.