How to properly configure DNS on a local network?

Question

Computer networks

Good afternoon!
There is a computer with 2 network cards. Works under windows OS.
1 network card - Internet through an external router (with addressing like 192.168.1.XX), the DNS server address matches the gateway (router address 192.168.1.1)
2 network card - local network (addressing 10.53.XX.XX)
In the local network segment there are 2 DNS servers (ie with addresses like 10.53.XX.Z1 and 10.53.XX.Z2)
There is a resource like sitename.ru located in the local network and having an address like 10.53.XX.XX.
When you try to open this resource through a browser, windows tries to resolve its name through DNS on the Internet network card.
The question is whether it is possible to force this sitename.ru to resolve through the DNS of the local network, i.e. through 10.53.XX.Z and not through 192.168.1.1?
Of course, you can register sitename.ru in the hosts file, but these are crutches

Answer 1

You just need to properly configure your local DNS.
Your local DNS holds the sitename.ru zone (with resolving records to local IP addresses), all it doesn't know is that it must forward to external DNS. Set up forwarding DNS for the local DNS server and use it everywhere - incl. and on your gateway (the one described in the problem) - it will make dns name resolution requests to the local DNS server, and it will resolve them through external DNS.

Answer 2

>In the local network segment there are 2 DNS servers (ie with addresses like 10.53.XX.Z1 and 10.53.XX.Z2)
Do clients have this DNS registered?
These DNS give the correct answer to sitename.ru?
Everything is checked with the dig utility.
dig sitename.ru
dig @10.53.XX.Z1 sitename.ru