It's almost certainly those photos that are filling her iCloud backup.
If she deletes them from the phone, the size of the backup will shrink in line with that and iCloud backups will resume without problem.
iTunes records devices, not accounts so you can back up as many devices as you like to the one machine.
Apple won't force you to upgrade your iCloud account to a paid plan with storage, but your phone will keep warning you if there's not enough space to back up your stuff to iCloud.
You should...