Personally, I'm not a big fan of docker, so only use it when there is no other option. As such, I have very little experience with it and am not completely clear on how it's networking works (although I assume that it just maintains it's own subnet).

FYI I have looked at "nginx proxy manager" previously and on face value it looks like a good thing. But because it's only available via docker, I have never used it and have zero experience with it or knowledge about it.

However, I would assume that it should "just work". A TurnKey VM is a pretty standard webserver setup and if "nginx proxy manager" doesn't handle a reverse proxying scenario like that out of the box, I'm not sure what the point of it is?! (Unless it's explicitly only for use with docker containers? - If that's the case you're out of luck...). TBH, it seems like pretty basic functionality for a proxy manager to be able to manage by default!?!

The only thing that occurs to me is that perhaps "nginx proxy manager" doesn't actually include Nginx itself? If that's the case, perhaps you need to install it on a server that has already has Nginx installed? Or perhaps you need to use it in tandem with a separate Nginx docker container? If it's not that, then I can only imagine that it's some sort of network config issue? If the "nginx proxy manager" docs don't cover that, then perhaps it's a docker config issue?

Regardless, I would imagine that doing what you are trying to do should be basic core functionality of any reverse proxy config. So I recommend re-reading their docs and/or asking for support on their support channel(s). Unless it only supports docker containers, then I'm sure what you are trying to do should be possible. Please feel free to cross post a link here if you do post elsewhere (so we can follow your progress).

Finally, unless you plan to be changing your reverse proxy config regularly, it may be quicker and easier to just manually configure one of your servers to act as a reverse proxy for any other servers you are also trying to host (even if you only occasionally make changes, that's still probably the quickest, easiest path - and doesn't require any additional installs or infrastructure). If you want some advice on that, please feel free to share info about the servers and services you wish to reverse proxy, where/how they are running and a little info about your network setup.