I agree, stay at either Moraine or Glacier Basin in the park. (We volunteered at Glacier Basin)
You said you only have a week.. I hope that's at least a week to do your three planned parks and not a week to and from home. If so..you're not going to make it.
Truthfully, for 7 days between the 3 parks, I'd eliminate either Great Sand Dunes or Black Canyon or just plan one night in each. They are small parks and you can really see the focus in a 1/2 - 1 day. There are short nature-type trails but the major ones are very strenuous.
Rocky Mtn. will have a lot more interest for you.
In re-reading your post it seems you are only going to have your motorhome and no towed vehicle. You are going to be very limited in what you'll be able to see. For instance at Black Canyon a highlight is to drive down a steep road to the bottom of the canyon. You won't be able to do that. It's hard to really see and explore a park without a towed vehicle.