In my estimation, despite being "dual purpose" most Dexters you find will be of a beef type. How many people even keep a family milk cow anymore? And how many of those keep something other than a Jersey, Holstein, or Swiss? Dexter dairy genetics are pretty few and far between.
Here in Southern Missouri, at least, it seems that everyone and their uncle raises Dexters. They aren't as numerous as traditional beef breeds and their crosses, of course, but they're far from rare. Don't make the mistake of automatically equating "heritage breed" with "rare."
As for traits, it all depends. On the whole, Dexters are quite maternal, but there is also a certain amount of individual variation. I've got one cow that's about as maternal as is possible, I think, and others that are less so. I've never had one that I'd consider in any way inattentive. As for how that works with your coyote population, that probably has as much to do with the coyotes as the cows.
Marbling of meat is partially breed-dependent, but probably more management-dependent. You can take a steer with great genetic potential and graze it on poor, coarse forage, and it may not marble a dime, or take a steer whose genetic potential is moderate at best but graze him well and get beautiful beef. And there is individual variation here, too.