How to copy files from one iPad to another under different iCloud accounts within the same family?

As understood, your wife has been using an iPad that belongs to an entirely different user (i.e. you). Consequently, all data stored on this iPad, from a data ownership perspective, belongs to the AppleID and iCloud storage of this other user (i.e. you).

Your wife has since acquired her own iPad - that was setup using her own iPhone. Both the iPhone and new iPad are associated with her own AppleID account and iCloud storage.

As is, you options are to selectively share your iCloud data with your wife:

Share files and folders in iCloud Drive on iCloud.com - Apple Support

You should note that folders and files shared in this manner still "belong" to you. If you stop sharing these files and folders, other users with which that data is shared will lose access to this data.

Alternatively, you can send a copy of specific files to another user by an available method - such as AirDrop, email, other messaging platform - or even physical USB media. Multiple files/documents might be combined in ZIP (compressed) archive file - and this archive file shared or sent to the recipient. When un-zipped, the individual files within the archive are unpacked on the target device - and, crucially, the unpacked files now "belong" to the recipient.

AirDrop supports sending individual files to another device, but not folders. The workaround to avoid multiple AirDrop transfers is to combine folders/files into a compressed archive file - and just transfer the single archive to the recipient. When received, the archive can be unpacked - restoring the folder and file structure:

Create or open ZIP files on your iPhone or iPad - Apple Support

A key aspect here is to understand the difference between sharing "your" data (albeit data created by your wife on your device) - and you sending a copy of "your" data to another user, in this case your wife.

Your Home Screen folders are created/set independently on each of your devices.

Unless you either use QuickStart to transfer all content and settings from one iPad to another, or restore an existing iCloud/iTunes backup to the new device (both of which will completely replace all data on the target device), your Home Screen folder arrangement cannot be "transferred" between devices.