What advice would you have for a military couplens strained by medical obligations?

Taking my heart out of the equation, It would be best for them to separate, being together is adversely affecting the children. If these are his biological children they will still be covered under DEERS, as long as he has them enrolled in DEERS. Once separation is in effect, send her back to wherever she is from, I believe her parents or someone would take her in until she gets on her feet, I am only speculating on this. He can then get bachelors QTRS as they are divorced (I am unsure on separation). He would have to pay child support, because he cannot have bachelors qtrs. and have children with him. This is the only way I see this being resolved unless these 2 can put aside their differences. For the kids sake either they need to cohabitate like decent human beings, or separate the Children do not need this extra stress of their parents fighting in front of them. My opinion only May be better opinions out there. Difficult situation you are a great PSG for working with this Soldiers issues! Remember when Soldiers stop asking you for help, they no longer respect that you will help them!!!! Great Job SFC Sutherland!

Bring the Soldier into the PSG's office for a sit down, and "come to Jesus" moment. Have him bring in his finical statements and LES for the last year in. Look in his counseling packet and see has he been sent to financial management and what was the outcome of that? Have him outline expenditures the family has, and explain any "needless" items that make no sense. This conversation has to be a "participative" counseling session being I need additional information to make an informed decision with his squad ldr, or section SGT.
While talking about finances, I'd bring up the issues with the marriage. Have they seen the chaplain, sought out marriage counseling? If not, I'd recommend they see one, the other, or both. If there has been ANY violence in the home (I'd probably do this anyways), I'd yank him into the barracks and he can see his children with a NCO present. In my counseling that I'd forward to the 1SG and CO, I'd put in there "You will not have ANY contact without a NCO present". "If you see your family out and about, leave the area. No hands gestures, motions with the lips of any kind, and no arguing". At this point I see that while I'd recommend counseling to them, it's a lost cause already, but I have to do my due diligence, and that includes walking his happy ass home to get HIS belongings. If possible the MP's would be there in support. Again he'd acknowledge there will not be ANY unsupervised visits with the family. If the kids want to see you at ANYTIME, let a NCO know, and you will be afforded the chance to be with them.
I've done two of these, and they're or were called EROD (Early Return of Dependents). It is a MESSY affair, it is one of the uglier things I've had to do, but to save the Soldiers, it had to be done. In this case, once I hear that there is no hope, then this would be done to her. Wherever she wants to go is fine, and the packout again would be supervised with a NCO with the Soldier, and MP's overlooking it all. Once compete and the family is out of the country, I'd rescind my no contact order being now he can talk to them on the phone, but any leave would be verified location wise. She would be told that she can still have the child's surgery there at the local Post hospital, and if none are nearby, contact TRICARE, and let them sort it out. The Soldier would make an allotment to his wife to support her (without breaking himself) and the kids until he PCS's or ETS's. With the family gone, my focus is to keep the Soldier busy and surrounded by friends who would look out for him, yet report to me any problems they detect no matter how small. My ONE concern is when the child goes into the hospital, the father is going to want to go, and he SHOULD go. I'm hoping that in the meantime he gets himself together and knows how to handle himself without us there, and the surgery is a success, he doesn't get into any trouble, and he comes back mentally effective and ready to do what has to be done as a Soldier. I'd hope that time apart would give them a chance to look at each other and think is this the best course of action; for US and the KIDS, and they decide to stick around with each other. If not, when he comes back, send him to JAG and lets get the ball on the military side rolling.

MSG (Join to see) Seems to me that, if the soldier cannot solve this situation on his own (and your involvement indicates he has asked for assistance or that it is impacting his duty performance and you became involved without his request), the chain of command should get involved. As a commander, if I was faced with this situation, I would probably direct that the family be returned to CONUS (ensuring they would be able to get medical care at a military hospital or through TRICARE), move the soldier in the barracks, and ensure his BAQ and other money goes to his family (yes, there are ways to ensure that). It would be much easier/better if they concurred with the idea, and I think a commander could convince them to. If the marriage is already in trouble, it seems best to go ahead and separate them (easier to do in an overseas location, as the commander can direct early return of dependents for a variety of reasons), while doing what can be done to ensure the medical issue is able to be taken care of.

The only other option I would give them is to solve their issues. If not, I would get the family out of country.

Although I never had this specific situation to deal with, I had several similar issues and all were worked out successfully (or, at least, as best as we could hope for).