There is no concept of "default domain controller for a site". In dssite.msc you'd move the DCs to certain sites. Based on this location, a DC's netlogons service will register site specific DNS records.
You can also get a DC to cover other sites than its own. Autosite coverage is where a DC would cover sites with no DC as long it has connectivity as per site links.
I'd recommend you use nslookup, set type to all and check _ldap._tcp.._sites.dc._msdcs.domain.com where you replace as appropriate based on whats in dssite.msc. Make sure you have only the right DCs registered against each site.
Also note that if you have cross forest resource access the calling server will be doing _ldap SRV record lookup based on its own site. if that fails it will do generic queries for _ldap._tcp.dc._msdcs.domain.com. You should get DCs to cover sites from the other forest as applicable. So if forest1 has Site1, Site2 and so on while forest2 has SiteA, SiteB and so on based on where the calling server is youl should ensure the DC covers the relevant site. See Administrative Templates\System\Net Logon\ for group policies to control site coverage.