Yes, the powertrain control module (PCM) would not work with the 3.5. When you mentioned TCM, that is the transmission control module and the BCM is the body control module.
I have to be honest. For this to work, you have to basically make the 2010 the same as the SS was. All computers, modules, vacuum hoses, wiring, and so on need transferred.
I'll try my best to help, but it is going to be difficult simply because of the variations between the two vehicles. I'm not trying to discourage you, but want you to be aware of what you are getting into. Anytime I have seen someone do this type of swap, there are always problems. Most commonly, a check engine light that will not go off which causes the vehicle to fail emission inspections.
Let me know what I can do to help. I'll give it my best shot. LOL
Take care of yourself,
Sunday, April 25th, 2021 AT 6:21 PM