Clearly the costs are high for a private school and this may make it very difficult with all 3 kids.
The advantage of the German school will be that all 3 kids will learn in the same style.
The school system in Bavaria is in my opinion old fashioned and very rigid. It is slowly changing with all day school now possible. If your kids can adapt it would probably be better to have them in the local system. You can always try it for 1 year and see how the 2 older kids cope. The youngest will be no problem as she can learn German at the kindergarten and by the time she goes to school she will be fine.
I took my kids out after primary school for a variety of reasons but this also has its problems as my kids could speak English but couldn't read and write it and the international school is all in English.
Hope this helps