If your iPad is near full (2 GBs of free storage space or less) this is but only one reason why your older iPad isn't coping well with iOS 9.
You need to backup all of your data on your iPad, either to iTunes on a computer, through Apple's own iCloud OR a dedicated Wireless WiFi hard drive, and then start deleting items off of your iPad.
You should start with paring down any music, movies and photos you may have on your iPad.
Then look at apps that you may no longer use and delete these (you can always redownload deleted apps at a later time.
Ideally, your iDevice should maintain a minimum free storage amount of 4- 6 GBs or greater on any iDevice (the more free space, the better) , plus, more than 50%-60% battery status to ensure proper operation, as well as, to ensure the possibility of a successful iOS upgrade/update installation.
In addition it is best to upgrade an iDevice connected up to computer running iTunes with you iDevice sync'd and backed up through iTunes rather than Over The Air (OTA) using a wireless WiFi connection.
I update ALL my iDevices connected up to Mac and sync'd over USB through iTunes.
My Mom"s and Wife's iPad 2s were still both on iOS 7.
I have NEVER, EVER had an issue with any iOS updates.
I did stay away from iOS 8 on the iPad 2s as NOT one iOS 8 update really ever seemed to completely solved MANY iPad 2 users still having a variety of performance issues... especially performance issues with speed/reponsiveness and random crashing.