I cannot testify to the academic achievements of any of these places, my kids went to the Dod School. But here is the information if you are interested. There is no way at all that your kids could go to the International School in Stuttgart or Heidelberg purely because the commuting time would make it nigh on impossible to have a life. There is an international boarding school in the Black forest but your childs ages make me think you would not really be interested in that!!
There is Faith Baptist School which is about a 15 minute drive from Landstuhl., Faith Baptist School is a private school and it has grades k through 5th. They use the A Beka curriculum. They also have art, music, and German class. It is located half way in between Ramstein AB and Vogelweh. Tuition is $3900 a year. Their phone number is: 0631-318-7519 http://www.faithbaptistchurch.de/school.htm
There is also a Montessori school between Ramstein and Landstuhl. C&K Children's House is a Montessori Preschool and Kindergarten that is located right outside of the West gate of RAB on your way to Landstuhl. Ph#06371-15127
You actually do still have the option of sending your child to the DoD school but ONLY if they have space available. Tuition is approx $20,000 a year. http://www.lans-ems.eu.dodea.edu/
Enrollement information is here including tuition fees http://www.eu.dodea.edu/enrollment/
There is also a British military school called St. David's in Ramstein (Up to age 11) Again they occasionally will take tuition paying children on a space available basis.
AGAPE Christian Academy is another private school in the area. They accept children grades K4-12th. They also use the A Beka Curriculum. Supplement to the curriculum, they offer a computer lab, music program, and Host nation language. They also have a Master level certified Special Education Teacher. This school is located in Ramstein Village and is right outside of the west gate of Ramstein AB. This is the e-mail address: AGAPEacademy@cs.com and their phone number is:06371-463440 Mon-Fri 8am-3pm http://www.agapeinternationalacademy.com/