Does a Power of Attorney have to be recorded with the county?

No.

In Florida the answer is no. I recorded the one I have for a friend because it can be accessed from any computer by going into the public records. That way, no matter where you are, if you need it you can pull it up.

The county where the principal lives. There are sometimes requests for an authorized copy which includes a seal from the register of deeds that registered it when conducting business. Having it recorded with the register of deeds makes it possible for people to look it up and make sure it's for real . Having it registered does make it look much more official. I don't know if is has to be recorded, but I think it is a very good idea to.

We did have it notorized by a notary, but need to know if it has to be recorded with the county recorder and which one? the county that we live in (the agent) or the county the principal lives in?

Has to be notorized. Usually with the County.