Thank you for allowing us to assist you with this problem.
I am sorry to hear about this problem.
Yes, it is true that the military will enforce civilian court orders of child support but the military does not actively seek out whether support is being paid just like a civilian employer does not make sure child support is paid.
If the child support arrears are brought to the attention of a soldier's Commanding Officer, that CO has the obligation to talk with her and make sure the child support is paid. Further, it is possible to obtain a court order where the child support would come directly out of the pay from DFSAS. If your husband is the one entitled to receive the child support then he would need to talk to the CO by writing a letter to where she is stationed to the attention of the CO.
Regarding children not living with her. If she is the custodial parent of those children by a court order, then she is legally allowed to claim them. However, if she is not the custodial parent by a court order, she is frauding the military but again, unless someone raises the issue there are just too many people to actually check each family.
Finally, when a military member has a medical condition [MedBoard] (including mental health conditions) which renders them unfit to perform their required duties, they may be separated (or retired) from the military for medical reasons. It is possible that she may be receiving a medical discharge from the military for some reason.