There's no such place as "between Corpus and Kingsville." If there were, it would be much like the place between your nuts and your browneye.
On a serious note, even if you are married with kids, you are still eligible for per diem while youre in Corpus as long as you DO NOT have your household goods delivered to any address here. You are, however, authorized to have a "partial delivery" of goods, so long as you tell the movers to separate what you want delivered and what you want placed in storage BEFORE they pack you up and move you out.
My wife and I had our goods shipped to storage, and specified the few items we needed delivered to our apartment. Best advice--find a somewhat furnished place in Corpus and draw perdiem while youre t44 training and deal with not having your household goods for a few months, THEN you can activate your PCS delivery of goods to any one of the multitude of housing options in the lovely K-rock Texas.