SOLUTION:
As most of you said, it appears to have been simple debris accumulation from the hard water we're hooked up to.
About 3 months ago we were getting low water pressure at the home where we're parked with full hookups. So, figuring that water in a residential neighborhood would probably be ok, I removed our water filter. Not much change in pressure, but I left it off.
And then the problem, as I described above.
I removed the easy-to-remove filters at the end of the nozzle on both sinks and it was thick with white gravel-like material. Cleaning that improved the flow somewhat in the bathroom, but not completely. As I was disassembling the bathroom faucet I broke a part and so had to buy a new one. When I installed it, flow was fine. So I have to figure something in the old faucet was blocked.
Now, what about the potty?
Mounted to the rear of the  bowl is a disc with holes in it, through which flows the water which fills the bowl, and which had become so slow. I had to remove the toilet, but I found the bolt which holds that disc in place. I removed it, shook the disc, and some white particles fell out. I couldn't disassemble it, but the wife soaked it in vinegar for an hour, and said that when she rinsed it, quite a bit of white junk came out. I reinstalled the disc, and the potty, turned the water on, and the flow is fine. We're fixed.
So....moral is, don't remove that external water filter. And when something like this happens, think first of the *easy* solutions. I just didn't realize we had such "hard" water, and that buildups like that were possible. And to have two unrelated outlets slow down at virtually the same time? Well, I probably should have bought a lottery ticket. Thanks much to all who contributed ideas and suggestions.
dave