Obviously your mother has an iCloud account now, so she will have to backup with iCloud first on the current iPad - and then restore the new iPad from that backup at the end of the activation process of the new device. All of her purchased content, app data and device settings will download to the device from iCloud.
How to backup and restore from a backupShe should read this as well for some helpful tips.You do need a computer at all when you restore from an iCloud backup. That's the idea behind going PC free with iCloud.
Something to try. Might work if you can "borrow" someone's computer.
Sync Your iOS Device with a New Computer Without Losing Data
How to Transfer Everything from an Old iPad to New iPad
I'll send that info to her and try to walk her through it on the phone. I didn't see a Restore option on mine, so wasn't sure what she'd do with the new one. She has a wireless printer, so she can print the instructions out to follow as she goes. Pretty cool for an 83 year old lady to get into tech stuff at this age!
Thanks for the help,
It's really very basic and simple to do. Did you read the second link that Tom posted for you? The one from OSX Daily? If she doesn't have a computer, there is no other way to migrate the contents from the old iPad to the new one other than what is described in that article.
I have no doubt that you will be able to guide her through it. If she can use the iPad on a day to day basis, she can get through this!