My family is arriving in the afternoon, and we were thinking it would be fun to explore DTD, and at some point take the monorail in a full loop starting from the DTD station all the way around back again. We don't want to use up a park hopper day that day however. Is this something that they accomodate?

I don't believe that's an option at Disneyland. (It is at Disneyworld, in Florida, though)

No. You would need an entrance ticket to board the Monorail.

The only way to ride the monorail is to use your hopper for the day, once upon a time long long LONG ago you could buy just a ticket for the monorail but that is long gone.

the key difference being that at disney world, it's a form of transportation. at disneyland, it's an attraction.