This is an interesting issue on a number of levels, but what I find so intriguing is that it basically involves a conflict between Federal law (under the military's Family Care Plan) and state law (under Kansas rules regarding child custody).
Now that being said. The service member's election to place a child in the custody of the other parent during deployment should not be looked upon by the courts as a voluntary surrender of custody. I also think they will probably find legal protections from having custody decisions made in their absence.