My router is (as of this weekend) a Diy, sff pc with slackware 15.
Mini-display, (small) wireless kb and mouse.
Wifi for wan, controlled by networkmanager for ease of management.
Ethernet for lan.
Custom iptables firewall.

It works for connecting to hotspots, and as a nat firewall/router.

But I want to run my (local caching) dns server on the router, instead of as separate hardware.

I installed Unbound 1.19.2 from slackbuild. Only to find out that trying to specify the ethernet port Unbound should listen on, or the wifi connection Unbound should use to send queries upstream - does not work if NetworkManager is managing those connections. Unbound reports a fatal socket error at load time.

I am thinking that having Unbound listen/forward on a virtual interface with a different ip address from the router's lan-side ethernet , should work? And maybe have Unbound running in a lightweight VM, if needed?

But I know almost nothing about virtualization or virtual network interfaces. Could anyone point me to some howto for doing this task in a basic/minimal fashion? It would be better if it only depended on what is freely available with slackware.

I think the issue you are seeing has nothing to do with NetworkManager itself, but rather with other service that is occupying udp (or even tcp) port 53. If you are using systemd then its own resolver systemd-resolvd must be the reason for it. If you want to confirm, issue something like the below: