PokerTracker

I am anticipating purchasing the license for the PT3 Omaha. I believe that once I do this, I will be able to apply the key or however it is enabled to my laptop, which is also running PT3?

Yes, you can use all purchased modules (holdem and/or omaha) on 2 computers that you own and operate.
If you already have a PT3 license for holdem then when you buy the omaha module all you need to do is restart PT3 to activate omaha.
If you're not yet registered then you will be able to enter the same code on both computers.