I have two iPads which currently use the same Apple ID.
When you say they "use the same Apple ID" could you please specify: are both devices signed into iCloud and the App Store using the same Apple ID? Because there is a difference. Every iOS device going back to iOS 5, I believe, has two distinct places to "sign in with your Apple ID," and this is not counting iMessage and FaceTime. Some people use the same Apple ID for both, some use two different ones, still others don't even sign in to iCloud but only the App Store. It's even possible to sign out of the App Store but stay signed in to iCloud. It should also be noted that older Apple IDs sometimes had "Alternate Apple ID"s associated with them, so it's possible that when you look in iTunes & App Store settings and compare the Apple ID there to the one signed in in the iCloud settings that they may list different email addresses that are actually associated with the same Apple ID. To find out how many email addresses are associated with your Apple ID, visit appleid.apple.com and click Manage your Apple ID. Look which address is listed for your "Apple ID and Primary Email Address," this will be the one shown whenever you log in to the App Store & iTunes Store (on iOS), or the Mac App Store, iBookstore, or iTunes Store (on a Mac. Or even a PC in the case of the iTunes Store). On the Apple ID page you may also see an "Alternate Apple ID" and/or an "Alternate Email Addresses" heading which will list the 'aliases' that might appear as your 'apple id' when you are signed in to iCloud with this apple ID account.
They will both need the same educational apps - I cannot see how they can do that with one Apple ID…. Will this erase the apps and pictures she has on there now?
Signing out of the App Store will not delete anything at all. In fact, apps should continue to auto-update even without the device being signed into the Store at all. Secondly, if a device is signed in to iCloud, signing out of it should also not affect any data except for email (and iCloud Drive. see *footnote at bottom of post). But if you want to be sure, turn off, one by one, Safari bookmarks, notes, reminders/calendars, email, etc. in Settings app -> iCloud. Each item you disable should give you the option of either
- keeping the local cache of data that was being kept in sync with iCloud, or
- remove (delete) the data from your device.
When you turn one of the iCloud items off, give it a minute, and then to be sure, hit the back button at the top left corner of Settings, then open iCloud again to make sure it has completely disabled that iCloud item (sometimes the toggle doesn't stick). If disabling each item goes well, you can tap Sign Out at the bottom to disconnect the device from the iCloud account/Apple ID.
Signing out in the iCloud settings as well as iTunes & App Store settings will completely disconnect the device from Apple services without deleting anything on the device—except for emails (if you were using an @icloud.com or @me.com email in the Mail app). It will stop backing up to iCloud, and if you ever specifically enabled the new iCloud Photo Library, (released in iOS 8.0), then obviously photos that haven't fully downloaded from the cloud will not be able to be downloaded without signing in to iCloud again
*The only exception to this might be apps which are using iCloud Drive (formerly Documents & Data), but if those apps have been opened recently they should have a local cache of their iCloud Drive files. Not all apps use iCloud documents/iCloud Drive at all. To see if an installed app is using iCloud for document storage, open Settings > iCloud > iCloud Drive. Furthermore, apps that have been previous downloaded, and then deleted, can actually leave documents in iCloud Drive. To see everything stored in iCloud Drive, from iCloud settings, tap "Storage _ GB Available" which should be right under the Family Sharing option, then tap Manage Storage, and look under Documents & Data. If there are more than five items here, tap Show All to reveal the totality of document "silos," which are usually (but sometimes not) titled after the name of the app that was installed and which created the data. You can also clean out iCloud Drive data by tapping an item, then Edit, then "Delete All" to remove that particular repository of iCloud Drive data. Or, some apps can list individual documents and you can delete only one or two of its documents without using "Delete All" for the app's data.