This is an all too common problem. Most hens don't do this when they go broody, they know to go back to their nest. But occasionally what you described happens. A hen is laying in her nest while she is out so when she goes back she goes to a different nest.
When this happens to me I toss the broody hen back onto her nest. I move her, not the eggs. Odds are she will go back to the original nest next time if it is not occupied. I've had really good hatches even with this happening though I'd really prefer it didn't.
Another way to handle this is to somehow lock the broody up so she has no choice which nest to go back to and where no other hen can get to her nest to lay an egg. In the pen you build you need room for a nest, food, and water. A broody hen should know to not go poop in her nest but she does not know to keep her food and water clean so give yourself access to clean things.
I don't know what your area looks like. Maybe you can build a pen around her current nest so you don't have to try to move her. Many people build a separate pen to move their broody hens to but there is a chance she will break from being broody if you do that. Still, there are techniques you can use that are usually successful. If you decide to do that get back with us.
All the eggs need to be started at the same time. When I get a broody hen I collect all the eggs I want her to brood and mark them with a black Sharpie so I can tell at a glance which eggs belong. After I start them I check under the broody hen after the others have laid for the day and remove any that don't belong. As long as you remove them daily they are good to use.
Good luck and welcome to the forum. Glad you joined us.