You can find most of the answers to your questions by going to the ky state police website.
To answer your question simply, KY doesn't allow the transfer of concealed carry licenses from other States to KY, and whatever training you took in Ohio to obtain your permit can't be transferred either. ( Except in very specific circumstances relating to peace officers and military personnel )
You have to take the class here in KY and go through all the hoops all over again. In addition, I don't know about OH, but in KY you have to notify the KSP if you change addresses within 30 days or you are subject to a fine. The guidelines also state that if you move out of state and are actually no longer a KY resident you have to inform them of that too, and your license may be revoked since you are no longer a KY resident. So you may want to check on that as far as your Ohio permit goes...
Just as an aside to awkward situations...in KY if you are pulled over, for example, you are not required to tell the officer you are CC, nor show him your license...I know in some states you are required to do so and just thought I'd throw that in there...they may ask for it, but you are not required to do so unless prompted. Just another reason it's a good idea to retake the class, especially if you change residency, as all the rules and regs are different state to state...