It seems that the live photo files need an application that natively supports the 2 "pieces" of the file.
Downloading from iCloud to a Windows platform seems to break that file into 2 pieces.
The MOV piece seems not fully compatible with uploading to iCloud.
Have you tried converting the MOV file to something else? Video file format is a huge black art.
Do you know anyone with a Mac? If you sign in to the Photos Application on the Mac and sync the local library using your first Apple ID, I would expect the live photos to be synced to the Mac in their "full" format. Then sign in to the second Apple ID and sync the library back to iCloud that way.
Long way to go, but that may work. Windows does not have an app, to my knowledge, that sees live photos natively. Mac does.