Ansley, I didn't know the answer to this question, so I googled military disability and child support.
After wading through some pages that didn't really apply, I found this website:
Disability Benefits | Child Support | Alimony | Divorce | Law Offices of LaVan & Neidenberg, P. A.
Here is the sentence I found very interesting and thought it may be beneficial to you: The Law Offices of LaVan & Neidenberg receive many inquiries about the court's ability to garnish a veteran's disability compensation. The short answer is, yes. There are certain circumstances in which the court can write an order to garnish your disability benefits.
So it seems that the court can garnish veteran's disability. I believe you would have to have a court order requiring them to do so. Check out the article. It specifically mentions child support garnishments. It's written by lawyers and it may give you some leverage and some info to take to DHS (if that's who you are dealing with).
Good luck!