Hi,
I'm a live-in nanny and regularly proxy parent for my boss when she's away on business. However, I look after school age children who never wake in the night.
As looking after little ones for this period of time is a huge responsibility, I would encourage you to discuss this with your nanny to see if she is happy to do this in the first place. If you were to get a temp you'd be paying them an hourly rate for the overnight, but as she would be live-in I'm sure an amount for the night would be more appropriate. There is no need to increase her daytime rate as she'd be doing this whether you were there or not.
As for an appropriate amount for the overnight, I would do some research online, and also have a chat with her. I know that a little generosity on the employer's part is always much appreciated when you are asked to do something a little unusual. It also depends on her experience and how often the children are likely to get up during the night. Paying her a little extra is bound to be a great deal more cost effective than taking everyone to Bali!
Also, you could give her the option of the days in lieu for perhaps either immediately after you get back (she'll probably want a break!) or to tag on to her next days off for a longer break. That is of course if you are offering her lieu time - you could always pay her extra to not take the days off. That might appeal to her - all nannies are different!
I hope some of that helps! Enjoy Bali