I looked up the German School; I found it very interesting. I expect that this is not just a language issue, it is the fact it is based on the German teaching curriculum that appeals to you; also, that your children will suffer a bit less from culture shock.
You will be commuting quite a distance from White Plains to Kennedy [
Driving Distance from JFK to White Plains, NY ] I am referring not to mileage, but to time for the commute. It is very congested on the roads if you are driving. If you are driving, the route on that link is probably one to consider. You really need someone from the White Plains area to help you with where to live.