When I do "nslookup or ping mydomain.local" in my local site the domain controller of the remote site responds not the dc of my local/current site.

This is not the issue,
the remote domain controller is the primary dns server for the dns zone yourdomian.locla
that is why that domain conroller is responding to nslookup and  ping

that is it. and that should be fine unless you want dns resolution to happen in this site
as dc are choosen by  clients and most applications (exchage) in the locat site only (whenever available)

In nslookup you get answer from first DNS from list in TCP/IP properties.
Check this list. Have you answer from first DNS in list?
May be it is server with multi network adapters?

We basically, don't want one site to query from remote site's DCs as long as the local site's DCs are working. Most of our sites are connected through a microwave link(E1) and we want to utilize that link for other purposes such as internet, voice, VTCs, and email. Workstations/servers should only query on its local DCs unless it is down. Is there any workaround to do that?

Thanks.

Works