First, you need to understand that there's a difference between "syncing" and "backup". Backup is the saving of content and settings, where syncing is the bidirectional transfer of content for an account to a web-based server (like iCloud, Gmail, Yahoo, etc.)
If you see your calendar in your iCloud account, that implies that you have set up your iCloud account to host (sync) your calendar, and perhaps contacts, email, and notes. An iCloud account can only sync one user's information at a time so it is intended to support a single user. You can have more than one iCloud account, and you can even have more than one iCloud account on the same device (but one has to be primary, and the secondary iCloud has limited capabilities), but a single iCloud account only supports a single user's content.
Backup is the saving of your device's content and settings to use in case you need to recover these things, but you can't see the contents of your backup (just the size and device name). You can backup more than one device to iCloud and you can backup to iCloud or you can backup to your computer, or both (one at a time though, you have to choose).
So, if your wife has her own email and calendar she can certainly do that in parallel to whatever account(s) you have for email and calendar. But if you have only one iCloud account then only one of you can use it for email, calendar, etc. But the backup of these accounts is really just a backup of the device's settings that link the device to these accounts. For example, if she uses Gmail then the backup of the iPad only backs up the fact that your iPad is set up to use her account, it does not backup the account itself (the content of her account is saved and preserved on Google's servers, not your device's backup).
Does that make better sense?
