Should I continue to let my sister walk all over me just to keep the peace?

OK. So I am the eldest of 3 sisters. My 'issue' is with my youngest. We used to be really good friends. But over the last few years she has been pushing everyone away and wont explain why! I would be 'ok' with that, except that she will treat me like Im a piece of rubbish until she wants her kids babysat, then she will be as nice as pie for a week or so leading up to the question, will ask me to babysit and its normally for a couple of days! The last time it happened it was at very short notice and it including her 7 week old kitten. The very next day after she picked them up she asked us to do something else. We couldnt do it on the day she demanded and that was it.... she absolutely spat it at us over facebook (no names were used, but it was very obvious who it was!) and I havent spoken to her since!

I would be 'ok' with this, but my mum lives around the corner from her and I live an hour away! Whenever I visit my mum, my sister is there, normally in a bad mood and just isnt fun to be around!! My mum knows what is going on, but her comment is that I know what my sister is like and that I need to be the one to 'make up' with her AGAIN!! But I dont think I can keep being the one who does the making up, only for her to treat me like a doormat until she wants a babysitter, and then continue to keep doing it after I have served my purpose!! She needs counselling for whatever is going on in her head, but she refuses to get it!!

Am I being unreasonable??? (I thought this would be a short question!! Sorry!!)