Alternative Access Mappings (AAM) issue accessing from internal and external URL's

Hi,

We have SharePoint 2010 with couple site collections. Our farm has following URLs (AAM):

For internal access:
intranet.company.local - all sites,
mysite.company.local   - my sites.

For external access:
extranet.company.com - all sites,
mysite.company.com   - my sites.

Then we access extranet.company.com using domain credentials on some sites we get authentication request for mysite.company.local. This is because we use some web parts that reference to My Sites.

But why we are asked credentials for mysite.company.local and not for mysite.company.comif we access extranet.company.com, how this can be changed?

Thanks