I noticed that each time Frodo restarted and obtained its ip-address and domain information, any multiple domain search options manually placed in its /etc/resolv.conf file would be erased.
Solution:
Edit nosmo's /etc/dhcpd.conf file's option domain-name line from:
option domain-name "shire";
to:
option domain-name "shire rivendell mordor";
Interestingly, this does not cause Frodo's /etc/resolv.conf to have multiple domains listed on its first line as might be expected.
root@kate:~# cat /etc/resolv.conf
# Generated by NetworkManager
domain shire
search shire rivendell mordor
nameserver 172.30.4.107