[UPDATE] I [25F] have had a huge fallout with my sister [24F], and my parents are now trying to get involved. Help!

Original post here - realised this isn't a solution sorry!
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TLDR: sister and I had a big fallout from her being a pain in the ass on holiday, she went straight to my parents, and now my Dad is also being a pain and expecting me to sort it all out, despite doing nothing wrong. Along with expecting family respect to be unconditional and that I should back family up no matter what(!)
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My dad eventually messaged asking if I had thought about going to see my sister this week with him, and suggested another weekend in a few weeks too. I said no to anything this week, and that it's my partner's birthday the other weekend.
Dad has now messaged asking if I could message my sister when I'm next in town, and that I should buy her a drink as "there is a risk of money issues now being a problem between you both". Also says "I know you have always been generous in the past", and "I know I am asking a lot by suggesting that you get in touch ... but I feel we have made so much progress in the last few days - and this seems like a relatively easy way to break the ice and draw a line under this episode. Will you do that for me?"
After all your replies on my last post, I'm realising how biased and one-sided all of this is. I'm not sure why I'm the one who a) has to get in touch, and b) pay for drinks!! Given it's my sister who caused the issues in the first place. I feel like I'm being guilted into sorting this out and I'm very nearly at a point of falling out with my Dad. This has really ****** me off :(


Source.