Domain controllers don't have local accounts though.
Tincan: I'd go with what MitchR is saying about having unique usernames in those domains and checking your trust, but I also assume that the account in domain D1 is in the Administrators group of domain D2? If not, do that. It should then work.
However, if you have to use 2 accounts, that's also an easy solution, and I use it on my side with no problems. Create an account: say, D1backup, and D2backup. Add D2backup into your service accounts list in Backup Exec on the backup server in question, and when you select a server, use the appropriate account.