When putting gas in my vehicle, the pump stops every gallon I put in. I have changed evaporated valve and vapor canister vent valve and its still not allowing me to pump gas.
It sounds like your shop is one the right track focusing on the emissions system’s evap hardware. When you pour gas into the tank there has to be a path to allow the air/fuel vapors already inside the tank to escape, otherwise there’s no room to allow more fuel and the pump shuts off. The usual design for OBD II cars (like yours, presumably ) is those gasses are piped from the gas tank into the evap canister, which holds the fuel vapors for later use, and vents the air segment of the gasses to the atmosphere. In your case the canister or the replacement parts may be faulty. Or one of the pathway’s pipes is pinched or otherwise blocked. Could also be a software control problem, wiring harness, faulty electrical connector etc. About the only thing you can do is to ask your shop to keep looking, and check for any stored diagnostic codes.
Note: I’m just a knucklehead diy’er with no experience with a 2010 Avalanche, just posting an opinion is all . Hope it helps.