i recently setup a new installation with ubuntu 18.04 and another with 18.10 at home. both installs had issues with resolving dns requests that my router would respond to. I have setup some dns overwrites in my home network so that for example wiki.psuter.ch resolves to the servers internal address when i am at home and it resolves my public ip when i am out of the house. however, ubuntu seems to ignore those overwrites.
i haven't had time to dig into what is going on exactly, but i found out that my resolv.conf doesn't point to my dns server. i therefore removed my resolv.conf and created a symlink to the one that systemd creates with the correct dhcp assigned dns server inside:
rm /etc/resolv.conf ln -s /run/systemd/resolve/resolv.conf /etc/resolv.conf