Hidden columns deleting

It sounds like you're using the autofill handle (the little black box at the bottom right of the active cell) when dragging the mouse across the screen. This automatically updates all cell content.

If you just want to select visible cells and copy/ paste those cells to another location, you can do so by selecting all the cells of interest (which will automatically include the hidden cells) then pressing F5. {This displays the 'Go to' dialog box}. Click the 'Special..'button and then the 'Visible cells only' radio button. You can then copy/paste and only the visible data will be pasted to the new location.

Alternatively, it may be possible to move the hidden cells to an unused location eg column ZZ or somewhere 'out-of-the-way'. That way they won't be modified and the cell references will be maintained when you move the original hidden columns.