I think this is an expected behavior because your SSL certificate is probably for s1.mysite.com. When www.s1.mysite.com is requested the host name does not match with the certificate common name, hence the warning. You should be able to workaround this by getting a certificate that contains both common...

WIth URL rewrite module you can redirect from http to https. Check out this post for more details: http://forums.iis.net/t/1149780.aspx You can also remove www from requests. Rules can access any server variable or header associated with the request. So you can have a rule that inspects the http host...