Rather than wait a week for the new power adapter, I decided to test the system with the alarm light and horn removed, and by just observing the operation of the relay. With no lead connected to the Vin pin of the Uno, the system appeared to work perfectly.
So, as suggested, the problem appears to have been caused by overloading the Vin.
Unless something else happens, at this time I believe the problem is solved and will make the appropriate notation in my original post.
Thanks, all, for your help.