Ghost there was a large age gap in my family and I feel I can relate to your daughter. Firstly let me say I think that the way she is speaking to your younger children is totally totally unacceptable.
I did school pick ups and child care ( properly a little more than your daughter) I enjoyed it and my parents paid me. But when I wanted I Saturday job I felt couldn't have one as my mum needed me. My a level revision and social life where impacted by childcare. Now the same would be said of a part time job but I felt trapped, like I had no choice.
I also felt resentful that sometimes I was the adult in charge and other times a child. Might sound silly now but finding your adult self is tricky at that age. if your daughter is a bit immature it could be even harder for her.
I'd make sure she knows she has to earn her money but allow her the choice to change "jobs". Outline that she'd have to give you fair notice (4-6weeks maybe). She may decide she's totally happy with childcare but it gives her control.
Also it may sound strange but I'd give her private time before trying more family time. At 4 your youngest should respect close door big sister needs private time / open door come on in. In return your daughter could put a few minutes aside (maybe after meals) look at all her siblings creations.
I'd really recommend spending some one on one time with her. My mum and I had a very fractured relationship when I was teenager. She had a baby I was 12 and 14, the first time I spent time just her and me after the babies was my 21 st. I really needed my mum a bit more.
As for family time I agree it is important, instead of telling her to spend an hr every week with you. Maybe ask her if she has any ideas how you can all spend at bit more time together? Finding something a 17, 12, 7, 4 and baby like will be tricky. She might surprise with her ideas. If her suggestions aren't great for littler ones maybe alternate activities so each child chooses?