Since in first post, OP did not mention another job for Dad, I made an assumption that Dad has been activated to active duty. I may possibly been incorrect but OP has not corrected any of us who have made that assumption and actually posted reference material dealing with military.
OP also said they were seeking legal aide from military, Dad is more than welcome to do that if Mom has not done that already. The military will talk to either spouse about the situation and give advice, but nothing beyond that, as they cannot represent in civil matters.
Adultery is usually not a big issue unless it involves other things, Example: another military member, Fraud (such as BAH), or unless non military member pushes the issue and causes difficulty for military within his/her Command.