You do not have to move. That is a decision for you to make. No one can force you to move.
It's my understanding that as long as you're married you also get base priveleges at any base even if you're not living on base or living with him.
One service that the Army provides that may be helpful to you is marital counseling.
You could call someone in the Army to learn about the rights of a wife separated from her husband. Your husband should have a number or he can get one.
As for getting a legal separation I recommend that you talk with an attorney. AS I recall my divorce attorney said legal separation costs about the same as a divorce and doesn't supply as much protection as a divorce. I went the divorce route. I've learned that if the couple have contracted debts together, even with a divorce, they are both still responsible until the debt is paid.
Frequently the first visit to an attorney is cost free. Not always. That probably is the first question to ask before setting an appointment.
Perhaps your husband is asking for you to go with him because he wants to try to make the marriage work. If you're interested at all in working on the marriage, I recommend that the two of you get counseling before you make the move.
If he reinlists will he know where he'll be stationed? Considering the war going on I suspect it's likely to be overseas. If he's not going to be with you, why move away from your community here?
This may or may not be a difficult decision for you. I recommend that you decide what you want to happen in your and your boys lives in the next few years and base your decision on that.
If you need more time to decide take as much time as you need so that you'll feel comfortable with the decision. Do what is best in your opinion.
I just found another of your posts that you made this month. He just left this month? He sounds unstable which may prevent him from reinlisting. He will have a psyc evaluation.
I wouldn't follow a husband who has given no consideration for me and my childern before quitting his job and moving out of state. Has he made any financial arrangements for you?
In the financial picture, if he is accepted into the army and you stay here you will get a separate check. Perhaps an advantage to him if you move with him and are living together is that he'll get one check and he doesn't have to have to get your input into how the money is spent. He'll be in charge.
For so many reasons it is in your best interest to get advice from an attorney about how to protect yourself and your children.
As to moving with him, it is not in your children's best interest to move. Life has been turned upside down already and a move would make adjustment even more critcal. Children need stability! And you need the support of your family and friends so that you can nurture your children.