Sounds like trying to use a rolled up newspaper to kill a fly. You can do it with janky restarts of your reverse proxy container, which results in down time of all apps, or you’d wait some long period of time for it to detect the change and rewire itself.
I’d recommend reaching for an electric bug slapper instead. Use something like traefik, where you can allow it to connect to your docker socket (just like watchtower), and automatically wire up the new container’s reverse proxy when it comes back online.