Timemachine - Turn off "No Backup for X Days" for secondary Disk
Since the backup volume is offsite, you can simply remove it from the list in Time Machine settings whilst it's away from home. When you add it back, Time Machine will pick up the existing backup. That's what I always do myself.

As for performance, the first backup after adding the volume back has a longer preparation step (presumably for computing the diffs) but that also happens anyway after a few weeks when Time Machine stops maintaining the diffs as changes on the file system occur in real time.