How can I get out of this!?

Alright, so basically every fight that my bf and I have is about me not making enough time for him, and spending too much time with my family. We live together and just got engaged (though we haven't told my family just yet). So, about at the beginning of the month, my sister asked me (in front of my entire family) if I could watch her 3 kids for 2 nights while her and her husband went on a getaway that they won in a sweepstakes. it would require me to make sure they have dinner, sleep there, and take them to school in the morning. Because it was in front of my whole family, I didn't want to just blatantly refuse and look rude. So I said it was a good possibility but that I would have to check my schedule and get back to her. Well, she ended up booking the trip before I actually confirmed. It's coming up this sunday and monday night...and my fiance is not going to be happy about me being gone for two nights. I can see that there was a misunderstanding and my sister had thoguht I said yes (and honestly, I never actually said no, because i forgot to "get back to her"!) and I don't just want to leave her hanging. But I also greatly respect my fiances wishes, and really* need to prove to him that he's my number one priority. I'm kind of looking for a way to gracefully (and fast!) look for a way to get out of babysitting. any suggestions?