Multisite going to wrong site

I have a multisite install of WordPress with two sites. In some instances, if I visit site1.com/page I will end up at site2.com/page. This seems to depend on the browser as it happens in IE and Chrome, but not in Firefox. It does not happen for the entire site (i.e. site1.com/otherpage works as expected). I can usually “fix” the problem by updating the page, but the problem will show back up at a later date and possibly on a different page.

Details of my multisite install: installed as a subdomain multisite. I have two different domain names. The second domain is a parked domain and points to the wordpress site. In the WordPress backend, I changed the site address to be the second domain name rather than a subdomain.

If you have any ideas on how to troubleshoot, I’d greatly appreciate your help.