Is it valid and recognized here? Yes.
Your laws from Alabama do not carry over here, So it would be best to brush up on the conceal laws here in KY again. The state simply recognizes the permit for the ability to conceal it, not how you can ie you must do so within the law of KY
However, If you have moved here for the long haul 1+ years, It would be very beneficial for you to start the process to received a Kentucky issue license. The process is simple , You can read
http://www.kentuckystatepolice.org/conceal.htm for all the information to get the process rolling.
I am not sure if you can hold "two" licences at at time, Most states require you to turn them in within xx days of leaving the state, others do not.
So in the case you do not receive your KY one or for any issue if you are asked you are just visiting KY, updated information on the licence is KEY.
The benefits of a Kentucky issued license only start with the most obvious.. Updated information... which is so important for more than the obvious... Like buying a Handgun from a dealer, which you wont be able to walk out of the store with if you do not have a Kentucky resident and ID / information to show. ( you may purchase a handgun from a KY dealer and not live in KY but the FFL you purchase it from will only SHIP it to a FFL in your residing area)
Hope this helps.