The issue is that the user is opening the VC client as "computerX\username" (their local login) but the VC server resides on a different domain where the user has credentials "domainY\username"
VC does not prompt for the AD login but pulls through the credentials used to open the VC client (in this case, the local PC username/password) which does not have permissions to VC.
ComputerX has no connection to domainY.
Preference is that VC allows a user to manually enter the relevant AD credentials to connect to a server.
This would also allow a user to run the VC client and connect to VCs on domainY, domainX, domainB etc, entering different credentials each time.