When two network interfaces are associated to an OpenStack instance, the Ubuntu precise guest will only configure the first one. Assuming the second can be configured via DHCP, it can be added with:
cat > /etc/network/interfaces.d/eth1.cfg <<EOF auto eth1 iface eth1 inet dhcp EOF
If the DHCP server answering on eth1 provides a default gateway, it will override the gateway provided by the DHCP server answering on eth0. The routers request can be removed from the list of default requests in /etc/dhcp/dhclient.conf
request subnet-mask, broadcast-address, time-offset, domain-name, domain-name-servers, domain-search, host-name, netbios-name-servers, netbios-scope, interface-mtu, rfc3442-classless-static-routes, ntp-servers, dhcp6.domain-search, dhcp6.fqdn, dhcp6.name-servers, dhcp6.sntp-servers;
It can then be re-activated only for eth0
echo 'interface "eth0" { request routers; }' >> /etc/dhcp/dhclient.conf