I think there´s no need to place the kids at an intl. school. The german education system provides special programs to learn the german language as a foreign language, called "Deutsch als Fremdsprache", or "Deutsch als Zweitsprache".
The programs are structured to migrate foreign nationals in Germany. You can attend classes for few Euros at "Volkshochschule, VHS", Goethe-Institut, even at primary schools up to Universities...
For Munich ask at KVR (Kreisverwaltungsreferat) Landeshauptstadt München - Welcome to the City of Munich
Department of Communal Services
We used to live in Bavaria for about three decades, you´ll love it too.