This is one of those funny fuzzy grey areas- is it a job or is it a family member helping out informally. It’s all starts out good natured and then everyone ends up feeling taken advantage of.
Think it’s best to make it as clear as possible. So I think that means deciding what it is. If it’s a job, then it’s market rates for a child minder or junior nanny not minimum wage. If it’s a family member helping out informally, then do something like buy her an iPhone or a laptop at the end, and give her bed, board and spending money while she’s there.
I honestly don’t think you can count bed and board as part of any remuneration/reward, as this is very much something you want/need, and she wouldn’t need the bed and board unless she was helping you.
In either case I think you’re going to have to be a bit more realistic about duration and hours of duty. So it might be that 2-4 weeks is more realistic than 5 weeks. And she should get to chose for how long.
You obviously don’t intend it like this, but what you’re proposing is a bit like a zero hours contract for a certain angle. Expecting a teenager to hang around for 12 hours a day to work a few hours “as needed” is something fast food places get castigated for.
So maybe expecting her to help with feeding lunch and tea, and look after your oldest every afternoon would be more realistic, whether that involves a trip out or just playing at home. Something like 12-5 or 1-6 everyday. That’s a big time commitment for someone that age, so it would need to be a job that pays her a decent hourly rate.
Or more informally, expect her to help out with lunch or tea, plus give you a couple of hours help a day at a variable time and say it’s a helping hand not a job and just treat her a lot and buy her a pretty big ticket gift at the end.
What you don’t want is a situation something similar to when people expect an au pair to be a nanny, and you end up with a stressed out/pissed off teenager as well as two young children.