I am trying to move hidden photos back to an album

Here's the problem: you moved the picture to the new album successfully, but it was hidden, so you couldn't see it in the new album!

If you go to the Hidden album, which lists all hidden pictures from anywhere in your library, and you "unhide" the picture, you'll then see it in the album you moved it to. It will disappear from the Hidden album because it's no longer hidden.

A picture can be listed in several albums at the same time. An album doesn't contain a picture-- an album is just a list of pictures you'd like to see together. If you have a picture in 3 albums, and you "hide" it, it will remain on the lists of those 3 albums, but you won't see it there. It will also be added to the list of hidden albums and can only be seen there.

By the way, if you drag a picture from one album to another, it doesn't move there. You just add its name to the list for the new album. It will remain on the list of the original album until you remove it from that list by control-clicking the picture and tapping "remove" or by selecting the picture and hitting Delete (which removes, not erases.)

bad advice I got told me making them hidden would remove them from the library but not both.

It depends on the system version and your device model. Perhaps you did not mention your system version, when you asked the question? It would have worked in the very early versions of Photos on a Mac and a bit longer in Photos iOS on the iPhone and iPad. Hiding a photo would just remove it from the Library (from the Moments), so we could temporarily remove photos there without having to delete them and make the Moments more manageable.

But in the current system versions a hidden photo is hidden everywhere, even in the albums and not just in the Library Views. Quite a few users requested this, because they wanted to use Hiding to keep confidential photos private, and so Apple changed the behaviour.

You don't say what iPadOS your are running, so your results may vary. Let's try this:

Do you see the Hidden Album? It's in Utilities, and it probably has a lock next to it. (If there are no pictures that have been hidden, then there may not be a Hidden view.) If you click on hidden and give your password or face ID, then you can see the hidden pictures. If you tap on one of them, for instance, then you can tap the three circled dots in the upper right, and you can choose "Unhide," there.

WARNING: It will disappear from the Hidden view, so you will have to go looking for it. Make a note of the filename or other identifier! If the picture is in some of your albums, then it will pop up there. It will re-appear in Recents, but in the original position of uploading, so it may be hard to find. I tested this before typing the answer, and, though I sort-of remembered the date, it took a while to find the picture!

Need to find a hidden photo of DML

How do you “unhide” a hidden photo on iPad? I cannot find any option.