The only reason "are military benefits welfare" is even a loaded question is because we have demonized government assistance and pretended that help from the government = handout you didn't earn. It is entirely possible to look at the military and consider the benefits a form of "welfare" without demeaning the benefits or looking down on them.
All government assistance programs are something that is earned, some as a society and some individually, and military benefits are an extension of that. You get benefits that you earned through taxes or service. You do your part to help others, and others do their part to help you. We all pay taxes to help each other, and we get money for food if we are in need. You provided a service to your country, and now your country provides a service to you.
Military benefits are a form of government assistance that you earned, just like all other government assistance programs. The only reason that should bother anybody is if they are looking down on government assistance because they don't understand how it works.
"From each according to his ability, to each according to his need," there is a reason why that statement fits both socialism and the basic idea of earned benefits by serving in the military.
Edit:
While the philosophical question of "welfare/earned benefits/contractual compensation" is very interesting, you also need to realize that there is a high likelihood that it is not really the source of your problem. There is a deeper issue between you and your wife than "are you a welfare queen", and you need to work on that before wondering what strangers on the internet think about you going back to school.
Talk to her, look at your own contribution to the household (if not monetary then physically), and make sure you give to her the same way you are giving to your education and gave to your country. She's your battle-buddy now, and you need to communicate with her to find out what is really happening.
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