how hard is it to prove a contract marriage?

If you have a legal marriage document (certificate, contract) from a US government entity, such as a US State or County, then you and your spouse are just that, married. Other people's opinion of your marriage isn't your problem. It's you and your spouse's responsibility to make the marriage work for you both. If you are having problems with the marriage relationship, I encourage you to seek counseling through the Chaplain, mental health clinic, or a civilian source.

I highly recommend Christian counseling, but this may not fit with your beliefs. My wife and I went through a difficult time at about the 10 year mark. We received good counseling and decided to work it out. We've now been married almost 55 years.

I never once questioned one of my sailor's marriages. If they had the paperwork, that is all that mattered to me. I do not understand all of the Army things you are talking about, but my advice is this: go talk to the JAG and the Chaplains (not for religious advice, but they have practical advice on how to deal with these situations as they have seen them over and over). If your command is hassling you over this, the IG may need to be involved, but go to the JAG and Chaps first.

There’s no such thing as a sham marriage. If you are married it is a legally binding agreement and there are responsibilities that go with that. For instance, providing financial support for your spouse and fidelity. The Army doesn’t care who you marry or why, only that once you do you conduct yourself as a married person.