It's been my experience that the priority setting(s) do not function ideally. For example, if you provide client A with the highest priority and all other clients have the default priority set, NetWorker, when it's prepared to perform a backup, says "okay, who's ready to backup now?" The client with the highest priority may not always be the first one to respond.
I have clients out there that have the following order specified:
C

:E:SYSTEM STATE:SYSTEM FILES:SYSTEM DB:
The system save sets ALWAYS BACKUP FIRST. I am not certain what NetWorker looks at for criteria when beginning a client, but I think, the same as labeling tapes, it will start with the smallest save sets and continue to the largest.
In this case, I would have to agree with mcurran1, however, it cannot be done in this fashion. If you attemp to create a duplicate client and add it to a group where it already exists, NetWorker will tell you the client already exists within the group. The only way to do it in this case, would be to create another group and add the duplicate client.
You might wish to check your parallelism settings as well, to ensure that your tapes are taking as many steams / multiplexing as much as possible. This might solve your issue as then you could have to the larger save set backing up at the same time as the reset. Optimizing the parallelism / target sessions can make a great deal of difference in some cases. However, it's a tricky process to determine the optimal settings for your network.
Good luck,
Carter Fowler
Hardware Service Technician
cfowler@amtelecom.net