If i was married to a military man and have a kid with someone else can i move without tge other parents permission with my military husband?

That all comes down to what your actual custody arrangements are. If the court granted the child's father ANY degree of custody, then you'll need his permission to move with the child. As a rule, the court won't allow a change of residence that will impact custody without the permission of the other parent. 

The military doesn't really have a role. You can be authorized on your husband's orders, but if the court won't allow you to move because of your custody agreement, then you can't go. It's not about the military, it's about the civilian court's ruling. Your husband is subject to going wherever his orders say he's going; spouses are a separate matter. 

Your first step is finding out EXACTLY what your custody agreement allows. It should dictate whether you can move without the father's permission. The next step is working with a lawyer to modify that agreement if needed (or possible). 

Be aware: If the court does not grant you permission to move and you do anyway (military or otherwise) -- that is a federal felony kidnapping charge. You can be prosecuted if you just up and move without the court's say so. 

I have a good friend who has been stuck in western NY for the last ten years, and she'll be there for at least another four. Her ex will not grant permission to move and her kids aren't 18 yet. 

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It is generally assumed that if a married woman gets PG the kid is her husbands. So the two of them have custody, regardless of who the sperm daddy is.

Not if the custody agreement  says otherwise.  Your new companion being military has zero bearing on it.  He goes where he is sent by the military  they don’t care if you are not allowed to join him

Does the father have any custody or visitation rights? If so, then NO you can't just frickin' leave.

yes, you can move anywhere you want

but you cannot take the child with you, unless the custody agreement gives you that right.

your new husband being in the military plays no role at all in the agreement between you and the baby daddy

i would ask a lawyer about this

Just marrying someone in the military does not mean you can go and leave the country or even state with the child. It all depends on the custody arrangements through the court system. Even with full custody some states will not allow you to leave the city or even state without permission from the other parent.