Can a mother take her children to another state and then files for divorce there?

If you're all Texans for more than six months, Kansas won't have jurisdiction to entertain your divorce/custody case until you and the children have been there for six months, and if the kids are taken there without your spouse's actual or implied consent (or at least without his objection), you'll have a jurisdiction problem even then. This area is full of reasons for caution.

You can usually file divorce in the court that has jurisdiction. You should look at the jurisdiction rules in Kansas before filing. Some states require a minimum residency requirement of 60 days or 90 days. Once jurisdiction is proper then you can file in those courts without repercussions.