Last time I visited Oxford there was this one boat sailing about her anchor (also known as horsing) so aggressively at first I assumed they were trying to brake the at anchor out. After a fashion, I guess they were.
Anchored with a combination rode (a little chin on the bottom and a lot of nylon rope) and perhaps 7:1 scope, judging from the angle of the rode, the boat was sailing back and forth over a dist of over 100 feet and more the 30 degrees from one tack to the other. Fortunately there was room, though any boats leaving the adjacent marina would have to watch their timing.
An over-sized tender on the foredeck makes an excellent sail.
Why so active? A combination rode doesn't help. It's light, does not rest on the bottom, and does little to damp the motion, as the wind catches first one side of the boat, and then the other. I'm not certain of the underbody, but I assume it was a fin keel design. But perhaps most critical was the oversized tender on the bow, creating windage forward as though they had a small sail hoisted.
A hammerlock mooring. Overkill, perhaps.
Solutions? In a strong breeze all horsing around could have caused real mischief. They could switch to a chain rode, which would quiet the boat at the cost of weight and handling problems (no windlass). A bridle might help, though not as much as it would on a catamaran. On a larger boat davits would move the windage aft, where it would contribute to stability. The tender could be deflated, although that is a hassle. They could use a kellet on the rode to add some drag, or drop a second anchor on very short scope (also known as a hamerlock mooring). A drogue could be added to the rode. They could set two anchors in a V.
A riding sail should help (as suggested by 2 commenters). In one sense they've always seemed counter intuitive to me; why would I want to add more windage if a storm might be coming? Additionally, only the v-sort (Findelta, Bannerbay Marine) seem like they'd be effective, and they're a little pricey ($375), take time to rig, add as much windage as a second dodger, and would need to be very tight in a real blow. I think I'd spend the money on some more chain. It doesn't need to be all chain, just more than they are using now. An increase from 10 feet to 50 feet should do it. That gives you mostly chain in shallow water, and enough nylon to avoid needing a snubber.
But they better try something, because if the wind had come up, nothing would have stopped then from popping the anchor loose and sailing right through a marina.