1) Are you comfortable shooting the 20 gauge you have? Do you think you can take the increased recoil of the 12? You'll want to practice, so make sure you can shoot it properly. I had my heart set on a 12, but when my wife and I went shooting, we realized it's a bit more than we're ready for, so we went down to 20.
Assuming yes, the 12 gauge can use a lot of specialty rounds and can use rounds which are just meaner to the bad guys (00 buck, which is unavailable to 20 gauge guns, for instance, and if you're looking at bean bag, CS gas or other crazy rounds, those don't come in 20 gauge at all). However, from what I've read, a 20 gauge is quite sufficient for most home defense encounters.
If I were in your place, and I were buying a weapon only for myself, not for my lovely bride (or more precisely, a weapon for myself in addition to my bride's weapon. If there's a bump in the night and my wife wants to make sure we closed the windows, I go down with the gun. If we're seriously worried there's a robber in the house and we want to hit him when we shoot, my wife gets it), I would invest firstly in training, secondly in a handgun. I can't shoot two shotguns, and a 20 gauge will do what I need to do. A handgun is a better backup weapon, and training is ALWAYS worth the money.
So yeah, as someone who is in the same place as you (owning a 20 gauge), my order of spending are:
Training & Practice on the 20 gauge
Another weapon for me so both my wife and I are armed
Practice
Training
Practice
Backup handguns and/or rifles to 'reach out and touch someone'
Practice
Training
Practice
Training
Practice
Whatever fun stuff I want to get because I have more money than time
Practice, Practice, Practice, Training, Training, Training, Training and more practice
A 12 gauge shotgun.
Unless you have some conditions you haven't mentioned (practice is free, you have more money than you know what to do with), I imagine that list is probably appropriate for you as well. If you do feel compelled to get a 12 gauge and have fired it so you know you like it, considering selling the 20 so you have money for practice (and training).