Yes, there's a big base there.
Kwajalein used to be the "target" for ICBM tests. I believe it's the same distance from Vandenberg to Kwaj as from silos in the midwest to the former Soviet Union.
They have missile tracking radars in place to map the precise impact point.
Here's a video of a Minuteman III test: https://www.youtube.com/watch?v=PDL_pIPScSI
You didn't say what kind of teacher, but I know they have contractor staff living there with their families.
He taught Science but I don’t know the exact certification. He graduated from Troy State Teacher’s College, now just Troy University.
He taught in Florida, Georgia and New Mexico. I guess they probably didn’t care which state you were certified in.
The more I think about it, I believe it was Ratheon.