Update for you bro.
Gimme a call this week so I can fill you in on the details.
I'm assuming you and your wife are in your early 20s or so.
Do you plan to make the military your career? (Don't dismiss this...I only did 4 years...if I had stayed in, I could have been drawing retirement and benefits in my 40s...I kick myself daily for not having done so.)
If you don't plan to stay in (or even if you do), is your M.O.S. in a field that you can use in civilian life?
Let them know (and make the commitment to yourself) that you will be using the education benefits, both while you are in and after you get out, to their fullest extent.
If they see that you both are making serious, well thought-out, future-conscious decisions for your life and that of your wife, it will be easier to accept.