Will the iPad 2 run iOS7 - Help. Grand-father in trouble!

Hay I need some help. A grand-father in trouble. I had given my iPad 1 to my grand-daughter a couple of years ago and she loves it. She lives on YouTube and is on it all the time. She also has a few games she loved. The problem was she was using my Apple Account and my YouTube channel. So all her favorites and history was showing up on my YouTube. I decided to get her an Apple Account under the Family Group. I set her up at the Apple Store and then today I reset her iPad 1 and set it up under her account. Boy what a mistake, Now the iPad 1 will not install any of the apps including YouTube because the iOS is at version 5 and will not update. It is crazy that the developers do not offer the older versions along with the newer versions. So none off her games will re-install and YouTube running thought her browser is horrible according to her. Sorry for the long post but here is the question. Can the iPad 2 get my out of the doghouse? If I purchase a used iPad 2 does it run iOS 7? Please Help. My grand-daughter is crying her eyes out.