Sister and I have always had a strained relationship. She seems cold and distant most of the time. Never any warmth from her however we stay in contact and plan things for our children to do together. I have 2 DC, 4 & 6. Her DC are 12 & 13. I looked after her kids one evening last month. I won't go into all the details but at one point my 13 year old nephew was misbehaving and winding little ones up, calling them names and swearing etc and I told him off. At end of the evening everything was fine and my sister came to pick them up.
The next time I saw my sister she told me I had no right speaking to her children in the way I did and they were crying for hours that night (??) because of me! She said I had ruined their week. I gave her the reasons for telling them off and she said I should have come to her first. I said they were misbehaving in front of me in my house so of course I told them off. Her 12 year old then interrupted in the background saying I wasn't her mum and how dare I tell her off! 
My sister let her speak to me in that way and then asked me if I think my kids always come to me whenever something is wrong and have a one sided view. I said maybe but they are 4 and 6, that's normal! I said they don't lie to which she replied 'oh yes they do!' At one point her 13 year old interrupted and my sister replied 'just don't hang around with (my DC) again.' I couldn't believe my sister actually said this. I also want to be clear the whole evening was not me telling her kids off, this happened 3 times max and I also told my own DC to play nicely etc and the rest of the evening consisted of them all playing a game then watching a film. They left smiling. I really am still in shock by this phone call. It seemed like a huge emotional outburst from nowhere. I later received a text message from my sister apologising saying she had a bad day (ironically she is constantly telling her DC off and seems stressed with parenting).
However, after this I vowed never to babysit again and to have a long break from communicating with my sister. I have just received another request to babysit her kids. After all she said I'm surprised she has even asked. How do I politely decline? I want to be firm and say I cannot do that after the last time and all that was said, which I'm still very upset by. But I also don't want another emotional outburst and all this ridiculous drama. Thank you!