any way to "re-sync" a bare repository against another bare repository?

Suppose I have a parent bare repository. I do a "git clone --bare" to create a child repository, and then clone the child to create a grandchild repository.

If changes get pushed into the parent repository, is there any way to cause the child to be updated?

Just a "git fetch <parent>" doesn't seem to help. If I set up parent as a remote branch I can fetch it, but then it shows all the branches as "parent/<branch>" rather than updating the child.

I just tried a "git clone --mirror" to create the child and it seems to allow me to pick up changes in the parent via "git fetch". Is that the proper way to handle this?

Thanks, Chris