I have travelled a lot of the years with families mostly for 2 weeks plus although at the end of a year doing a 20 hour flight, 5 kids, 5 weeks away and some of the weeks is road trip I'm super excited and dreading it at the same time :)
It really depends if it's holiday holiday or a second house type situation. Half of my travel is going to a second or third house in another country so would just work my normal hours in a different country but if it's more of a holiday situation I find I work a lot more cause there are day trips, dinners, weekend activities etc.
All flights, travel insurance, food, entries to zoo/parks etc, transport is all paid by you, which you've already said you'll be doing.
Normal salary is obviously a must. If it is going to be normal hours you don't technically need to pay anymore, it really depends what you can afford.
Previous bosses for me have normally given me a bit more each week around 100 pounds sometimes a bit under just cause I'm not at home and can't go out and do my normal thing with my friends etc.
If sharing a room with child I would charge overnight fee (even if child sleeps all night) cause I'm still on duty and can't go out
I think you need to sit down with your partner and think what would make holiday most enjoyable for you... ie nanny has weekends off or works through them (either gets money or time off when get home), how much extra you can pay (if can afford to do any)
It is definitely harder when working on someone elses holiday, and my employers understanding that is what helps me enjoy myself and be happier. Just my boss saying I know you've been working long hours have a lie in tomorrow morning makes a huge difference.
I think the main thing is work out with nanny what you are doing before you leave obviously she'll have to be flexible but if she's incharge when you are around or just there for an extra pair of hands, if she'll be in charge of cooking etc etc.