Advice needed for handling DNS server setting

BobAGI

I have an OpenVPN server set up with 2 services running on ports 1194 and 1195. It runs on Ubuntu 16.04 LTS.
Version: OpenVPN 2.4.6 x86_64-pc-linux-gnu

The 1194 one is running a full tunnel with all traffic running through the VPN server.
The 1195 instance is a split tunnel server where only traffic to the office LAN runs through the tunnel.
All other traffic goes through the client's own gateway to the Internet.

So far I have not set up how the DNS server should be connected to the client and I am looking for advice on how it should be done. What I need is to tell the client the name resolution for the local servers on the internal LAN, which are known by the domain controller (a Windows Server 2012 machine).
I have seen a server side directive:
push "dhcp-option DNS 8.8.8.8" in some discussions, if I replace the IP with 10.0.0.5 (the local DNS server) will that work in both of my cases?
I want to be able to both resolve local addresses on the server side LAN and for the 1194 instance also Internet addresses.
But for the 1195 case I do not want external addresses to be handled by the server side DNS if possible...
Can this at all be accomplished?
Below are the two server side conf files:

port 1194
proto udp
dev tun
ca /etc/openvpn/keys/ca.crt
cert /etc/openvpn/keys/VPN.crt
key /etc/openvpn/keys/VPN.key # This file should be kept secret
dh /etc/openvpn/keys/dh2048.pem
tls-auth /etc/openvpn/keys/ta.key 0 # This file is secret
topology subnet
server 10.8.0.0 255.255.255.0 'nopool'
ifconfig-pool 10.8.0.2 10.8.0.127 255.255.255.0
client-config-dir /etc/openvpn/ccdw
ifconfig-pool-persist ipp.txt
push "route 10.0.0.0 255.255.255.0"
push "redirect-gateway def1 bypass-dhcp"
keepalive 10 120
cipher AES-256-CBC
comp-lzo
max-clients 20
persist-key
persist-tun
status /etc/openvpn/log/openvpn-status.log
log /etc/openvpn/log/openvpn.log
verb 4
explicit-exit-notify 1

port 1195
proto udp
dev tun
ca /etc/openvpn/keys/ca.crt
cert /etc/openvpn/keys/VPN.crt
key /etc/openvpn/keys/VPN.key # This file should be kept secret
dh /etc/openvpn/keys/dh2048.pem
tls-auth /etc/openvpn/keys/ta.key 0 # This file is secret
topology subnet
server 10.8.1.0 255.255.255.0 'nopool'
ifconfig-pool 10.8.1.2 10.8.1.127 255.255.255.0
client-config-dir /etc/openvpn/ccdl
ifconfig-pool-persist ipp2.txt
push "route 10.0.0.0 255.255.255.0"
keepalive 10 120
cipher AES-256-CBC
comp-lzo
max-clients 20
persist-key
persist-tun
status /etc/openvpn/log/openvpn-status2.log
log /etc/openvpn/log/openvpn2.log
verb 4
explicit-exit-notify 1

BobAGI

I have tested to use the DNS option on the full server by adding to the push lines so the config file now looks like this:

port 1194
proto udp
dev tun
ca /etc/openvpn/keys/ca.crt
cert /etc/openvpn/keys/VPN.crt
key /etc/openvpn/keys/VPN.key
dh /etc/openvpn/keys/dh2048.pem
tls-auth /etc/openvpn/keys/ta.key 0
topology subnet
server 10.8.0.0 255.255.255.0 'nopool'
ifconfig-pool 10.8.0.2 10.8.0.127 255.255.255.0
client-config-dir /etc/openvpn/ccdw
ifconfig-pool-persist ipp.txt
push "route 10.0.0.0 255.255.255.0"
push "redirect-gateway def1 bypass-dhcp"
push "dhcp-option DNS 10.0.0.3"
keepalive 10 120
cipher AES-256-CBC
comp-lzo
max-clients 20
persist-key
persist-tun
status /etc/openvpn/log/openvpn-status.log
log /etc/openvpn/log/openvpn.log
verb 4
explicit-exit-notify 1
This has the effect of showing the DNS as 10.0.0.3 in Windows when doing an ipconfig /all command.
So the push actually works, but the function is not there..
If I comment out the entries for a few local servers on the remote network in my hosts file I can no longer ping them by name. By IP address is OK but not by name.

So my problem is not only to get DNS working in a split tunnel configuration, it does not work even in the full server configuration when adding the push commands as described in the OpenVPN manual...

TinCanTech

I presume you have a DNS server installed ?

BobAGI

That is what I was told.
So I logged on to that server (10.0.0.3) and went to Administrative Tools/DNS to verify and to me it looks like it holds a database of a whole lot of hosts ikncluding the ones I tested ping against.
They told me to set DNS for VPN to point at 10.0.0.3...
But it results in what I wrote above.

Edit:
I logged on to a few other servers on the network and checked their DNS settings via ipconfig. All were using 10.0.0.3 and on all of these ping to a named server worked.
So what is causing a PC connected via OpenVPN and where it is getting DNS as 10.0.0.3 too to fail when pinging other hosts by name? The strangest thing of all is that there is someone replying to the pings from outside of our network (seems to be from Network Solutions). How can this happen?
On servers inside the network ping to an unknown host results in "could not find host", not replies from Network Solutions...

TinCanTech

TinCanTech wrote I presume you have a DNS server installed ?

BobAGI wrote That is what I was told

I suggest you verify this with who ever "They" are ..

All openvpn does with DNS is push DNS server(s) IP and/or domain to your client ..
the rest is outside the scope of openvpn.

BobAGI

OK.
I have found what caused the bogus ping returns now.
Turns out that my Asus router had a domain name (same as the target remote network) in the DHCP settings.
When I removed that the false returns disappeared.
But this just causes a not found ping return when I have removed engineering from the hosts file:

C:\Users\Bosse>ipconfig /all

Windows IP Configuration

   Host Name . . . . . . . . . . . . : AURIGA
   Primary Dns Suffix  . . . . . . . :  <== Here there was a domain companyname.com
   Node Type . . . . . . . . . . . . : Hybrid
   IP Routing Enabled. . . . . . . . : No
   WINS Proxy Enabled. . . . . . . . : No

Ethernet adapter AGI OpenVPN:

   Connection-specific DNS Suffix  . :
   Description . . . . . . . . . . . : TAP-Windows Adapter V9
   Physical Address. . . . . . . . . : 00-FF-56-1B-E5-C0
   DHCP Enabled. . . . . . . . . . . : Yes
   Autoconfiguration Enabled . . . . : Yes
   Link-local IPv6 Address . . . . . : fe80::74cb:69ac:c6e2:a264%19(Preferred)
   IPv4 Address. . . . . . . . . . . : 10.8.0.2(Preferred)
   Subnet Mask . . . . . . . . . . . : 255.255.255.0
   Lease Obtained. . . . . . . . . . : den 1 november 2018 17:11:08
   Lease Expires . . . . . . . . . . : den 1 november 2019 17:11:08
   Default Gateway . . . . . . . . . :
   DHCP Server . . . . . . . . . . . : 10.8.0.254
   DHCPv6 IAID . . . . . . . . . . . : 654376790
   DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-17-BD-6A-0A-EC-9A-74-FB-B9-CF
   DNS Servers . . . . . . . . . . . : 10.0.0.3
                                       10.0.0.7
   NetBIOS over Tcpip. . . . . . . . : Enabled

C:\Users\Bosse>ping engineering
Ping request could not find host engineering. Please check the name and try again.

The IT people at the company is from an outside firm, outsourced network maintenance.
I will try to get hold of someone there.