I've never done the under deck thing, but I did do just a simple solar cover real out of pvc and a couple of mounts. You could accomplish what you're describing in a variety of ways DIY if you're creative.
I think what you might want to do is figure out what the main issue is with getting DW to put the cover on and figure out how to solve that with your solution. Are you assuming that the hidden reel is going to make it easier so she'd do it, or are you just trying to make it easier in general, knowing it falls on you?
That pool cover rolled up is probably going to be 12-18" in diameter without popping the little bubbles, so you'd need some room.
Is there some hard and fast rule that says you have to roll the cover up? What about doing a ribbon type deal, where you effectively weight the one end, which would drop into a long narrow hole in the deck (long enough to accept it without folding across), you drop that in, and lay it in layers, then pull it out the other way. Taking pvc and putting it every 8' across would give you "fold points" to keep it in place, and then it would come out pretty easy. Add a long enough lead rope to the top pvc so that you could reach it and pull it out and over the pool. Just on idea.
I've seen a solar cover on the Internet, on YouTube, similar to your description but they rolled it up and a reel that had huge thingies sticking up for each piece of PVC to lay in. The rolled up cover was huge in diameter. I don't know what the point of the PVC was. :?
Your idea sounds interesting. So what is the process getting it out of the pool please?
If you want something motorized, almost any sealed electrical motor with enough torque (ebay) could be used to roll it up. If you want a redneck solution, you could fit a bolt on the end and use an 18V screw gun (this is what we do for our RV jacks.)
I'm facing a similar delimma, and so far, my plan is to build a storage "box" on one end of the pool that hinges and holds the cover reel (also diy), but blends in to the deck (composite decking.)
Thanks for the great ideas people. People keep them coming please.
I'm leaning towards a solar cover to use at night, mainly to keep a lot of blowing stuff out of the pool for at least 10 hours or so. That way I could turn the VF pump even lower for circulation without needing as much pressure to keep the Pool Skim sucking 23/7. An added benefit would be reducing some heat loss which we usually don't need here, normal summers.
I like the box idea. My shallow end concrete decking is only about 24", then a foot further of medium sized river rocks, then a wood park fence. I thought about mounting the reel on the fence post (they are very sturdy) and concealing it with a box, bench like, with the reel feeding out the bottom (hinged top for maintenance). Then put a crank mechanism on one end, even using your idea of a motor, maybe solar powered. I have several panels panels and small controllers laying around that would pretty well keep a small deep cycle battery topped up. Or to start use an electric drill, as you have suggested. I'm particularly fond of Li-Ion batteries these days for most of my battery hand tools. Just make a spot in the box to store the drill.
I'd have to mount mine pretty high, for two reasons. Mastiffs are pretty tall and my boy bounces around as if he was one of the Labradoodles, so we don't want him bumping his noggin. Also, I like to be able to see the dogs, through the fence when I am sitting around the pool. Another option would be the tool box idea, with part of it below ground. I've been thinking about taking that part of the fence out anyway. Why go with just bench type concealment when it would make a great place to store poles and other pool equipment. The only drawback for me would be that it would be one other place for snakes to den. That wouldn't be to hard to take care of, using some type of material to line any vent openings.
Good luck!