I agree she should have her own room, at the very minimum. If she doesn't get that she literally won't get ANY time off. That might be OK for 2-3 days but for a week that is way too much to ask.
I would definitely NOT ask for at total amount for the week, because that leaves room for the mom to use her for as many hours as she wants. The hours, or at least the maximum hours, should be very clearly agreed upon in advance. Otherwise it's a slippery slope and your daughter could end up feeling taken advantage of. It's only fair to your daughter and to this mom to lay out everything in advance and make sure everyone is comfortable.
Beyond that, it all depends on how much your daughter wants to do this. Assuming she is happy to go and earn the money, but not necessarily crazy excited about these particular destinations, she should get:
--her own hotel room, or at the very least her own bedroom in a suite/flat
--all travel costs
minimum and maximum daily hours specified and agreed upon before the trip say minimum of 7 and maximum of no more than 10
--£7-9 per hour for all hours worked, and your daughter should be paid for at least the minimum amount even if for some reason the mom doesn't use her. I would ask for £7 if your daughter is keen to go on the trip and wants to see the places they are going, and closer to £9 if she's doing it solely for the money
daily stipend for meals and incidentals the amount will depend on the cost of things at the destination, but should be no less than £25-30 per day
--In the event of any emergency, e.g. your daughter gets very ill, or you have a death in the family, the mom will pay any additional costs to send her home immediately, or fly you out there to take her home, or whatever is appropriate under the circumstances.
--There should be an agreed-upon minimum amount that your daughter will get even if the trip is cut short for some reason, as consideration for not making other plans. Say £250-300?
If she is really excited to check out these particular cities, she might settle for something on the lower end of the above, but MOST importantly everything should be clear and agreed upon in advance, to avoid any misunderstandings.