I believe your regular Relief managers who work for you weekly or fortnightly should wear your uniform.
When I owned motels all staff including the cleaners were required to wear the uniform.

Now we are starting as Short Term relief Managers relieving Motel owners/managers when they are on holidays. For this we have our own shirts. My feeling that this approach is professional and at the same time let's the guests know that we are not the regular owners/managers. It isn't a "cop-out", more of an explanation if we are not up to speed on local tourism and such.