OP, a few things need to happen here if you want to keep your nanny, and to keep her satisfied.
1) If you cannot find a substitute family for your maternity leave, you should really consider paying her something, even if it is not the full rate.
2) Do you know what the other family is planning to pay her while you are on leave? If it is only their usual half, then... yikes. Major ill will to be had.
3) As far as raises going forward, considering you all seem to be very happy with her, two things need to happen IMO. The first thing is an earned raise for her tenure and excellent performance on the job. You and the other family should discuss this. The second thing that should happen is a raise for the third child. So, for example, consider raising her rate for two children to $22/hour. Then, add an additional $2-3/hour for the third child, bringing her to $24-25/hour. Just as an example, but I think those would be good amounts to bump her by, too.