Thanks for your help. The reason this is an issue is that for some reaosn my XX@icloud.com (actually, it's XX@me.com) is not mine, it's my girlfriend's. She also has an iPhone and the iPad at home is set up for her Apple ID.
For some reason, our two accounts have this link.
I guess none of this would be a problem if we could just delete both accounts and start all over. But, my nderstanding is that this will have repurcussions for iTunes and our iPhones (apps, etc.). Neither of us have started using any of the XX@me.com or XX@icloud.com emails yet - we simply use out gmail and hotmail accounts.
What is the prurpose of the 'alternate apple id'?
The me.com and iCloud.com addresses are one and the same. It sounds to me as though you are using the same Apple ID for your iCloud account, this is often not a good idea.
You can use the same Apple ID for your iTunes account and continue to share your iTunes content and other apps and books, but I would consider using separate Apple IDs for your iCloud account so that you do not mix up your contacts, calendars etc.
The iCloud email address is a feature of iCloud, you do not need to use it if you do not wish to do so, but it is necessary to create this address in order for you to use iCloud notes.