Once you backed up your iPad to iTunes, disconnect the iPad.
From the Settings App Under the General Settings under Reset select Erase and Reset ALL contents.
The act of doing this should return your iPad back to its factory "out of the box" state and you should see the iPad welcome screen.
Proceeed to set up the iPad as new, from the iPad, the way you would if the iPad just came out of the box.
Test its performance for a little while on your network with nothing else on this iPad!
See if it is running better from a reset factory state.
Setup of your Mail app. Do some web browsing on Safari. See if online videos run, etc..
Basically, use the iPad in its basic state.
Then, after some time, reconnect your iPad 2 to your computer running iTunes (it DOES NOT have to be an up to date version, but at least an iTunes vers. 12.6.x version) and do restore of your iPad's data.
If your iPad 2 returns to a slow state then, some data in the backup maybe corrupt.
You will have to repeat the reset of the iPad once, again.
You may have to re-sync your data in small groups of apps and small groups of images/music and videos until you can isolate the cause of the iPad 2 slowndowns.
You may just have to redownload apps and depending on the data thst you might have stored in your downloaded apps, if the data stored is minimal OR not that important to you any longer, forget the data and redownload those apps as fresh versions and test on your iPad.
Good Luck to You!