A better response would have been "Sorry but your mother does not actually have the authority to declare federal disasters"
Your "better" response isn't funny and violates the basic rule of improv comedy, which is that you go with what the other person gives you, instead of contradicting it. As an actor, Reagan was certainly familiar with this.
It's pretty much what people would expect Reagan to write if it had been a serious request warranting a reply. What isn't expected, and makes it funny, is the humour of actually replying and pretending to take the letter seriously.
I think it'd lose its humour if it was markedly out of character and didn't sound like a serious reply.