Hi,
Allowing the using of external DNS sever with among other external recourses like external websites (on the Internet) would really go hand it hand.
And for Internal recourses I imagine you wouldnt even need the external DNS server.
So I would imagine that you lack a NAT Translation for the VPN Pool towards the Internet
An example configuration to NAT the VPN Pool to the "outside" interface IP address of the ASA while accessing Internet through the Full Tunnel VPN Client would be
object-group network VPN-POOL
network-object 10.10.10.0 255.255.255.0
nat (outside,outside) after-auto source dynamic VPN-POOL interface
Also you will have to have
same-security-traffic permit intra-interface
This will allow the traffic to take a "U-turn" on the ASA "outside" interface and head back to the Internet.
The NAT configurations format depends on your current NAT configuration. It should work with the above but there is always a possibility that some current NAT configuration might cause problems for it or override it.
Let me know if I understood your situation correctly.
If this solved your problem, remember to mark the question is answered.
Naturally ask more if needed
Hope this helps
- Jouni