Maybe you could use CNAME Record like this:
client1.com CNAME client1.test.com.
shop.client1.com CNAME client1.test.com.
The dot at the end is to tell the DNS not to complete your entry with the default-Domainname.
If you not must use an DNS to redirect, you also be free to use You even could do it by IPTables Forwarding. Good at this solution... you can decide which port will point to which ip... this way you could forward webserver to the Server of your Customer, but leave Mail at your server (for example)
Here how forward a port to another host that has an external IP:
sudo iptables -t nat -A PREROUTING -i eth0 -p tcp --dport $port -j LOG --log-prefix="PreRouting $port..:"
sudo iptables -t nat -A PREROUTING -i eth0 -p tcp --dport $port -j DNAT --to $ip:$port
sudo iptables -t nat -A POSTROUTING -j MASQUERADE
sudo iptables -A FORWARD -p tcp -i eth0 -o eth0 -s $ip --sport $port -j LOG --log-prefix="S Forward $port.."
sudo iptables -A FORWARD -p tcp -i eth0 -o eth0 -s $ip --sport $port -j ACCEPT
sudo iptables -A FORWARD -p tcp -i eth0 -o eth0 -d $ip --dport $port -j LOG --log-prefix="D Forward $port.."
sudo iptables -A FORWARD -p tcp -i eth0 -o eth0 -d $ip --dport $port -j ACCEPT
You also have to add this command to set on your network stack:
sudo sysctl -w net.ipv4.ip_forward=1
This will work in a default DENY IPTables setup.