Best thing is to show the other license and just play dumb!
In other words, you want to break the law by (1) driving in another state when you do not have a license that permits you to do so and (2) present a license to a law enforcement officer in that other state that you know is not valid since you know it was cancelled. Not exactly what an upstanding, law abiding citizen does, it? It doesn't make you really any better than any other crook who tries to commit some offense because he thinks he'll get away with it.
Moreover, you take a risk in doing that; should that officer from that other state indeed see from the computer that your license is not valid outside Alabama, you may be cited or even arrested for that. In addition, if convicted in that other state on the license offense that may then lead to the suspension/revocation of the Alabama license you just worked so hard to get.