Setting up a local DNS server but clients that use it can't access the internet

I was wondering if someone would be as so kind to point me in the right direction for what I am trying to achieve.

Basically I have local clients that are a mixture of windows and linux, these clients need to be able to access the internet for updates and so on, but to also access services that are on the local network by a hostname that has been setup correctly I believe on the local DNS server.

The clients are able to use the dns server when specified as a nameserver on linux in the resolv.conf file and as a dns server on windows, I have only tested this with the linux clients at present but when they are using the local dns server as the sole name server the linux clients can do an nslookup on domains such as google for example, and get google's ip address. So it would seem as that internet access works, but when trying to do updates from apt-get this fails as ***.debian.org fails to resolve to an ip address, and nslookup debian.org doesn't work, no ip address is returned.

The local domain and subdomains that are setup on the local dns server do work, the clients are able to access the correct services, in order for the linux clients to do updates the isp name servers have to be put back in resolv.conf then updates work, and then the file has to be changed back to the local dns server once again.

I have followed the ubuntu guide at the link below, and yes I realise I am not using ubuntu and using debian instead, but as these are both debian like and/or based distro's I didn't think it would be an issue.

https://help.ubuntu.com/lts/serverguide/dns-configuration.html

I am not sure if this is relevant, but each server and client has two network cards the first network card is for internet access only and DHCP addresses are provided to that card, the other network card is access to a vlan that the servers and other clients are on, no internet access is possible through the second network card. This setup isn't something that can be changed and so the solution would need to work with this setup.

If someone is able to point in the right direction I would be ever so grateful!

Thank you.