Thanks for the chance to assist.
Can he get in trouble for lying to the military.
Short answer: Yes. Art 107, UCMJ
makes false official statements illegal. IF he has made a false official statement, the military can indeed prosecute this.
Longer answer: While a false official statement is illegal, its not clear that happened. The military will not look at the % of time he has the kids to determine compensation he gets...if he has court ordered support, he will rate BAH
(housing allowance) at the higher "with dependents" rate. So I bet he never had to make a "false statement" to his command...he only had to show them his court order to pay custody
and they will pay him the full BAH.
If in reality he has only a few days a month, then take this case back to court and get the court to modify the orders (custody AND support)...if you have them most of the time, you rate more money.
Please let me know if you have further questions; if so I will do my best to answer them. If not please hit the accept button, its the only way I get credit for my work.