Why does installing rdnssd remove network-manager?
Take a look at apt show rdnssd
Look for the Conflicts line:
Conflicts: network-manager
There's your answer: rdnssd and NetworkManager cannot exist on the same system simultaneously. They conflict.
FYI: Ubuntu Server and Ubuntu Core use systemd-networkd instead of NetworkManager. Unless you have bolted NM on, rdnssd should work well with those versions of Ubuntu.