My dog would be shaking by anxiety. Aquatic adventure would be more of a horror trip to her

Welcome to the coldest summer for the rest of your life :)

Since you already got a lot of ELI5s, here is a basic to-do to get you up and running. From my experience, since I use the exact same setup as you describe.

1. Set up your containers in a way you can reach them from you local network (e.g. http://123.456.789.10:123)
2. Get a domain name (you can get one at the registrar of your choice, e.g. mydomain.com)
3. Set up NGINX proxy manager (NPM) (default address of webui would be http://123.456.789.10:81)
4. Set up a new proxy host in NPM:
   • Domain name: mycontainer.mydomain.com
   • Scheme: http
   • Forward Hostname/IP: 123.456.789.10 (if you get an error later on, you can use the docker container name if NPM and your container are connected to the same Docker network)
   • Port: 123
   • Via access lists you can provide a very basic username/pw login to protect your sites (you can do more and cooler stuff with Authelia)
   • In the SSL tab you can (and should) setup the SSL encryption: https://www.youtube.com/watch?v=TBGOJA27m_0
5. Go to the DNS management of your registrar
   • Add an A-record for mydomain.com and the public IP of your server (you can google public IP to find it out)
   • Add a CNAME record for the subdomain with name mycontainer and target mydomain.com
6. open port 443 of your server in your router If everything worked right, you can visit mycontainer.mydomain.com, your DNS server will resolve this to your public IP and forwards the request to nginx, which will serve the data of your local container