Quality issues streaming remotely

Sounds like your setup might be limited to an indirect/relayed connection.
This could be a restriction due to your internet connection or a bad remote access configuration. You should be able to confirm that from the dashboard.

Did you already have a look at the related troubleshooting support article?
https://support.plex.tv/articles/200931138-troubleshooting-remote-access/

There’s also a guide with some more details on how to identify/resolve remote access issues.