The short of it is this: In the United States, your Verizon Droid Incredible 2 (DINC2) will only work on Verizon. It will never work on AT&T / Cingular / T-Mobile.
It is possible to SIM-unlock your phone (Verizon will do this for you for free if you call their international services department, provided you have been a good customer for 6 months with them). Once you've done this, you can put other carriers' SIM cards in your phone and switch it to global mode (aka 'use the SIM card' mode) and you are no longer using Verizon; you'll be using whatever carrier corresponds to the SIM card in your phone. This is great if you're traveling to Europe or Asia, since you can get prepaid SIM where you're staying and use it. But it doesn't work in the USA.
As I understand it, there is a radio lock (i.e., a hardware lock that cannot be overridden by rooting / unlocking / jail-breaking etc) that prevents you from using AT&T / Cingular / T-Mobile SIM cards in your DINC2 when you are in the US, and the reason is explicitly to prevent you from using non-Verizon networks in the US. It sounds like this is what you're trying to do, so I'm sad to say, as far as I know, it won't work. You must use Verizon service while you are in the USA; if you want to switch to a different carrier in the USA, you must buy a different phone, because your Verizon DINC2 is radio-locked to the Verizon network. Pretty lame, huh?
(again, if you are outside of the USA, you can certainly use different GSM carriers provided you've SIM-unlocked your phone with Verizon. I do this all the time).
Hope this helps.