I realize you have more experience but my brief attempts at baby sitting have not been good from my view. I had to baby sit a boy and I hated it (he was a destructive monster) without asking since I was friends with parents and they said I'm good with kids.
But I was better at controlling him because I do not have any love interest. It was a chore but I did ok. I did baby sit a few LGs and it is more difficult for me. I do not fall in love with every LG, but I somehow give them more freedom. I was a bad baby sitter there (nothing happened to the child, but there were a few broken things in house).
Your last sentence desribes the baby sitting after that. Sibblings, a boy (5) and girl (7). They get along nice, but kids will fight. I tried to be neutral, but sided with girl. In objective, she was right but I am not court and should just not let them fight.
Now, I think I got a hang of it as I am the main baby sitter for the LG I'm in love with. That is why you have to view both my answers to 1 and 2 and combine them. It is hard to tell her NO and order her what to do. And then puppy eyes like she is disappointed with you. That is hard.
That is what I mean. I like to be a friend with LGs but when baby sitting I am also the one responsible for them, traditional adult / child roles. If you are emotionaly attached it gets harder.