To ensure that the People Picker in SharePoint provides results from all appropriate domains, open the SharePoint Management Shell as admin on one of the application servers, then run the following command.
stsadm -o setproperty -pn peoplepicker-searchadforests -pv "domain:domain1.corp;domain2.corp" -url "http://sharepoint.example.com"
In each command, include all domains separated by semi-colons for each URL desired. Repeat for additional URL’s if desired. I do not believe it is necessary to run for Search and MySites site collection URLs as they do not use the people picker in my experience so far.