Multiple computers running Nginx, each has multiple domains, one router.

Hello,

My name is HiM29 and I'm having problems setting up 5 different computers with Nginx under one router.
Each computer uses at least one domain and one computers had 3 domains configured in Nginx.

When I try to assign port 80 from the router to each server the firewall will not work probably and this even had influence on other opened ports. The firewall probably crashes or refuses to work, I can't confirm this as my router's web interface doesn't allow that much access.

I am thinking of this solution:
Setup a DNS server and assign each domain name a local domain name to each server. Set the local address of the DNS sever as first choice in the router's DNS configuration and in it's own DNS configuration. And redirect each request from a domain name to a local domain using Nginx. Each server had access to the outside.

Is this a correct solution/ and is this the best solution?

Yours sincerely,
HiM29