The woman should speak with a custody lawyer in Germany, to make sure that her removing the children from that country would be permitted. I understand the background you have provided, but German courts historically prefer that German children be raised in Germany - and she should be aware from the outset if this could affect her custody orders.
If you were to marry in Germany, you would apply for her to come into the United States on a K-3 spouse visa. You would apply for K-4 visas for any children under 21.
Most U.S. school districts have ESL (English as a Second Language) programs of various sorts. Check with the schools in the area where you intend to live about their ability to accommodate German children with limited English language skills.

