MacOS – Time Machine Problems

No.

Time Machine will just start backing up your Mac along side your old Backups. Your previous machine will be back on Tuesday (or whenever last backed-up) in your timeline, with the new machine after that.

Basically, I would recommend not trying to constrain time machine to only a weekly interval on the offsite drive.

That being said, you can have both drives work totally independently as that is how the software is engineered. If you really only want a weekly snapshot, only connect the weekly drive once a week and force a rotation of the destination:

 tmutil startbackup --rotation

Once you have a backup to the weekly drive, eject it and send it away. As long as all dives get reattached every 14 days or so, you won't get a warning dialog that any are out of date.

Again, you can certainly enforce a single weekly backup by the procedure you follow but two things make that practice less needed than you might expect:

• The backup intervals are very low space overhead compared to the size of cheap backup disks.

On my worst Mac, the system averages 5 MB of overhead for system log files so in absence of user files changing, you have 24 daily and 31 monthly snapshots you would avoid storing 275 MB (or 0.0003 of a one TB drive) if you were on a strict one per week schedule.

Since the cleanup of old backups is so fast and the storage impact so low, most clients with offsite rotation end up just swapping disks each week and let the software cull the extra snapshots per the normal schedule, leaving weekly snapshots more than a month old.