This is possible , now called CEA(Day), but, normally only after boarding school allowance or CEA (Board) has been claimed for a full acedemic year. If you have extenuating circumstances it may be possible to get special authority - best to speak to your RAO in the first place.
BSA/CEA is very vulnerable if personnel kick the a** out of it. Forces only get the allowance if the parents travel the world & stay living together. If parents want to live apart there is no reason the children could not attend the local comprehensive and live at home with their parents or relatives. Private/indep school is the biggest retention tool for officers. It is in the Treasury cross-hairs.