WordPress network and cookies

If you use different domains in your network the cookie domain should be dynamic so users can login to each site.

define( 'COOKIE_DOMAIN', '' );

If you still having issues with logging in, pay attention to the www prefix. Update all domain references with a www prefix.

define( 'DOMAIN_CURRENT_SITE', 'www.yoursite.com' );

This www prefix should also be added to the wp_blogs and the wp_site database tables.