There are many states that require you to have an in-state license in order to take a traffic school or defensive driving so that a ticket can be adjudicated or points not be placed on a driving record. We know of no exception for military families but since states vary on their laws, you can check with Kentucky and Texas to see if there is some special regulation that applies to you in this situation.
Speeding 16 mph over the speed limit in Kentucky is a 6 point offense according to the Kentucky Driver Point System. Since your license is from Texas though the TX DPS is the one that will note the speeding citation on your TX driving record.
Kentucky and Texas are both members of the Drivers License Compact. As members of this agreement their courts and departments of motor vehicles will exchange information regarding traffic violations and inform the state in which a person is licensed of traffic infractions.
According to the Texas Department of Public Safety they will place out of state offenses onto your TX driving record. The Texas points system lists that it is 2 points for a moving violation conviction in Texas or that in another state. Points however are not assigned for speeding less than 10% over the posted limit or for seat belt convictions. Points accrued remain on the driver record for a period of three years from conviction date.