What to do if I’m a soldier and my husband wants a divorce?

If neither of you have filed for divorce and there are no custody orders in place, then you can go get your children and relocate them with you to your new duty station.  It's not against the law to move to a new state with your own children.  Where many people get into trouble is when they take off with the kids to avoid the requirements of a court order-- that is a felony in Texas. 

"The without legal problems" is the tricky part of your question.  Yes, legally you can move and take the kids.  However, if he files for divorce and is granted a temporary order before you relocate with them and that order restricts the children's residence to Texas, then the matter will get somewhat more complicated.  In the event that he does get a divorce moving quickly, you should make plans to respond quickly to the filing so that you can get the restriction lifted.  Things you can do right now include holing away some funds for a family law attorney, making sure you have a good plan for child care at your new duty station, and mapping out a parenting plan for your new residence.  A parenting plan is things like how you are going to make sure the kids get their homework done, providing them access to extracurricular activities...basically anything that shows you are on top of their needs and you are more than prepared to take care of those needs.  His argument, of course, will be that you're going to be too busy with the relocation to take care of the kids... so the more pre-planning that you do now will help counter that argument if/when he files.

If he does file and you are mid-stream in the relocation process, you may be able to get extra continuances if you need them because of your status in the military.  When looking for a family law attorney, try to find one that has had experience in representing military family members so they can help you with some of these exceptions and tailoring a case for the judge based on your military background.