After being a werewolf at night, how to prevent becoming naked

You've likely hit a bug.

While you've agreed to help Sinding, it doesn't lock in your choice: if you attack him at any time before the end of the quest (when the curse is removed from the ring, allowing you to take it off), you lock in your choice to help Hircine.

However, doing so is supposed to go down differently: you act as one of the hunters and chase Hircine through the grotto, ending with you skinning him. He's not supposed to appear in jail.

You can try that: kill him in jail and skin him. If that part isn't bugged, Hircine should appear and complete the quest for you. As a reward, the ring will disappear.

Otherwise, welcome to a Bethesda game, where crippling bugs like this are par for the course in the first couple of weeks after launch.

From what I've heard and experienced, your followers are predetermined to wear a specific kind of armor. For example, if I give Lydia light armor, she won't wear it, even if she has nothing else equipped because she is preset for heavy armor only.

I did experience a similar issue with Lydia, though minus the nudity. I tried to give her a light armor helm. I would see her wearing it right after I equipped her with it, but after a couple of fights, it was gone. The item was still in her inventory but she simply refused to wear it. I believe this is because the light helm does not meet her armor requirements. In your case, regular clothing would not fit your housecarls preset armor specifications so they are simply unable to keep these items equipped.

That said, I don't think there's anything you can do short of using the console to force her to wear it.