MWhen she tries to reset the password Apple says that no such email-address is known to it. When she tries to create a new ID Apple says that those email-addresses are already in use.
When you manage an Apple ID, you can associate an "alternate email addresses" with it.
IIRC, when you do that, the situation you typed above applies.
You can't create a new Apple ID with an "alternate email address" (it'll tell you that it's in use), and you can't reset the password for it (since it's an "alternate email address", not an actual Apple ID).
On her iPad, if she goes into Settings > iCloud, is the Apple ID listed there the one she's using when she tries to reset the password? Also, she could be using a different Apple ID in Settings > iTunes & App Store, so it's going to depend on what she's doing when the iPad asks her for the password as to which Apple ID applies (if she's using more than one Apple ID on her iPad).