I managed to come up with an answer to my question, so I thought I might just as well share it here if it helps someone else.
I have yet not solved how to access Islandore through my local network, but through adding my domain name in the .env file (DOMAIN=
my-domain.org) and then rebuild and run the new docker-compose.yml file (make -B docker-compose.yml && make build && docker-compose up -d) I can now access ISLE through the domain name I specified in the .env file (yes, I also needed to link the public DNS-entry with the local IP-address of the VM where ISLE is installed). Luckily I have an authentification system in place, so it's still possible to contol who has access to ISLE during this initial development phase.
// Theo