OK, on a slightly more serious note. OP, lots depends on the employment contract and working relationship you have with your nanny (the main one, not the back up one.) My nanny has a contract which says she may take the same number of days a year holiday as I am given by my employer. I work 50%, so get 14 days leave. My nanny works 50%, so she gets 14 days too. 4 of those are Bank holidays and that's when she takes them. 5 of the other days I choose, the remaining 5 she chooses, but is to choose before my work roster is allocated in order to allow me to accommodate her holiday by ensuring I get those days off work. This is set out in her contract and was agreed when she first started working for us. So there are no surprises to either me or my nanny.
If you have a good working relationship with her, she will surely see that you are going to have a baby in the summer. Why not discuss the possibility with her now that you would prefer her, just for this year, not to take her holiday in the month your baby is due. In most normal working environments, people ask their boss for holiday but if they are busy then, the request may not be granted. Eg, I work in the travel industry - it's really hard to get Christmas, Easter or the school holidays off because it doesn't suit my employer, and a friend works as an accountant - year end (March-April boundary) is very difficult for her to get leave. If you nanny has children in school, perhaps she would like to consider taking her main family holiday at Easter or summer half term this year? You are giving her plenty of notice.
Next - wtf is your children's father? Why is your daughter going to be alone for 6 days with a woman she doesn't know (if Nanny No 2 is there.) I'm taking it you are having a planned CS at a hotel private hospital with that length of stay. (Unless you have a medical problem, in which case I apologise for my insensitivity.) I had an EmCS and several other problems, and was out of hospital in 5 days with baby1. If you are having a planned CS, your OH should have that written in big red letters in his diary already, and be with you in hospital when you want a visit, and at home to make breakfast for your other child and to read her her bedtime story. In this case, your other child should be fine with another person looking after her for a bit. If your OH is NOT going to be around, leave the bastard now, divorce him and take half his (apparently) considerable cash!
If all of us have read between the lines, and in the background of your 'woe is me, I'm going to be down to my last 2 private childcare professionals for a couple of weeks - how will I manage' is actually a story of you needing help because you are severely disabled or something, it would probably have been worth you mentioning this. Otherwise people are just going to have a little giggle about how the entitled few live. Let's face it - not having one's regular nanny because you can't sort out an employment contract properly is a bit of a first world problem, isn't it?
Fwiw, I have a nanny, and had a private midwife and a housekeeper when I had baby2. I had reasons other than 'I am loaded and I'm worth it,' some of them medical. I just didn't feel the urge to come on here and have a weird stealth boast about it!