Why not use a completely separate repo for each child-theme site once its established? Clone the master repo when spinning up the environment, remove the Git directory, init a new Git repo, and push it up to wherever? Now each child theme can be developed independently of each other.
Alternatively, if you’re using the same site as a base and making minor variations based on geographic location or whatever, have you considered making it a multisite? Might make it easier to maintain.