You can have apps from 2 different Apple IDs on one device. When you go to update the apps it will require the password for the Apple ID that was used to download it. If it is a free app just download it on your iPad without switching accounts to avoid all the confusion.
Why are you using 2 different Apple IDs?
If you log out of the currently logged in account and then log in with a different account and re-download one of its past purchases then you risk tying your iPad to that account for 90 days : http://support.apple.com/kb/HT4627
Do you sync both devices to the same computer ? If you do then you should be able to sync the app via your computer's iTunes (if it's not on there then you can copy it from your iPhone via File > Transfer Purchases). If you sync them to different computers then you can copy it from the iPhone's computer (you can see where it is stored on that computer by right-clicking the app in the Apps part of your iTunes library and selecting 'show in explorer') to the iPad's computer (you will need to authorise that account on that computer's iTunes) and add it to its iTunes via File > Add To Library and then sync it