you can't force refresh but you can forward all old ip requests to new one. for a website:
replace [OLD_IP] with old server's ip
replace [NEW_IP] with new server's ip
run & win.
echo "1" > /proc/sys/net/ipv4/ip_forward
iptables -t nat -A PREROUTING -d [OLD_IP] -p tcp --dport 80 -j DNAT --to-destination [NEW_IP]:80
iptables -t nat -A PREROUTING -d [OLD_IP] -p tcp --dport 443 -j DNAT --to-destination [NEW_IP]:443
iptables -t nat -A POSTROUTING -j MASQUERADE