I don’t know how easy it would be to migrate to your own local machine, but what you’re describing sounds like Desktop-as-a-Service. All of the major cloud providers offer this in some form.

If you expose port 80 on the PiHole service, can you login? Are you certain it’s a problem with Traefik? The PiHole could just be having problems.

You might also look into the 302 redirect that PiHole does upon login. It might not play nicely with Traefik.