Check Engine - P0700 and P0601

Hi all - I'm new to this forum and I'm hoping that one of you knowledgeable people might be able to help me out. My 2012 Chevy Equinox LS 4 cyl is having a sporadic issue with REALLY slow acceleration. Yesterday, the issue occurred but this time the check engine light came on and I noticed the drive letter (P, N, D, etc.) was flashing. While it was in this state, I also noticed that the SUV would shift hard between P, N, and D. After letting the vehicle sit for a minute, I started it back up and it drove without issue to the auto parts store to get the code read. There were two codes pulled from the vehicle, P0700 Transmission Control System and P0601 Internal Control Module Memory Check Sum Error. Has anyone on here dealt with this issue before? Searching other forums, it sounds like it could be a communication issue between the PCM and TCM. Is this something that I can take to my local shop or is it better suited for a trans specialist or the dealership? I tried reseating the cables into the computer that sits on top of the battery and after a few starts, the check engine light did cleared. Any thoughts on this would be greatly appreciated. Thanks!