You've already set your second iPad up just like the work one, yes? If you want to keep all your apps you'll have to keep the account. Unless there is some reason to keep the accounts separate, say the business owns the other account, just keep using the same one. You can set up the iPads differently, and on different computers.
But once you do, remember which iPad is on which computer, and only sync them with that computer.
Go to your home computer, download the newest iTunes. Go to the Store menu and authorize it. go to the sign in link top right and sign in with your account. Don't make a new one.
Plug in your iPad. It will come up and say it's associated with another computer, and would you like to erase everything. It should also give you an option to Transfer your Purchases. If it does, choose that. If it does not, just say no. Then go to the File menu and choose Transfer Purchases From. . .
When this completes you should see all your apps in the iTunes library, and any media you may haver purchased from iTunes.
It should let you sync normally now, and you can set your new iPad up anyway you like with as many or few of your old apps as you like.
You could have done that on your work computer too, btw. The each device can be set up differently. But now you have the convenience of playing with the settings and sync options of your home iPad at home.