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> Rotate backup storage
We alternate between two homes. Could we keep separate Time Machine backups in each?
Time Machine has a feature known as rotating backup storage that should be ideal for this, and is easy to set up.
Start by installing backup storage systems in both your homes, preferably using local connections — although this also works well with storage shared over a network such as NAS systems.
When you’re at the first location, add the storage to Time Machine as a backup destination, configure it in System Settings, and let Time Machine make its first full backup before continuing with automatic backups as normal. When you then arrive at the second location, repeat that process, adding the storage there so your Macs can back up to both. Time Machine will then make another first full backup, and continue with subsequent backups until you return to the first location. It will then resume making backups there.