windows - How to setup NS Record to External Name Server from Internal DNS

We have the following scenario:

1. Our company has an Internal DNS & an External DNS server.


2. Both of them holds the same domain (example.com).


3. Our Internal DNS is a Windows Server that cannot access the Internet, but has setup forwarders for "All others DNS" to the External DNS


4. We need to setup a sub-domain (vendor.exmaple.com) to an Authoritative name server (ns1.vendor.com) from vendor and the vendor will provide the IP-address for this sub-domain.



5. And, we have setup the following in our External DNS for Internet people who needs to access the name (vendor.example.com).

   
   
   

   vendor IN NS ns1.outsider.com
   
   

So that when Internet people queries the sub-domain

nslookup vendor.example.com

It returns with the corresponding IP-address defined in our vendor name server (ns1.vendor.com)

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Now, we encountered the problem that:

If we apply the same setting into our Internal DNS server, we got "Server fails" when an internal staff uses 'nslookup' to query "vendor.example.com" when going through the Internal DNS.

If I use 'dig' with '+nssearch' to query from my PC to our Internal DNS,

C:\>dig +nssearch vendor.example.com
;; reply from unexpected source: #, expected #53

;; reply from unexpected source: #, expected #53
;; reply from unexpected source: #, expected #53

; <<>> DiG 9.9.5 <<>> +nssearch vendor.example.com
;; global options: +short +cmd
;; connection timed out; no servers could be reached

We expected that when the request goes to our Internal DNS, it will forward the request to our External DNS and get the IP-address from the vendor name server. Then, respond to the PC inside our company network.

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Could anyone tell me what's wrong on this? And, how we can this correctly?