This is not mentioned in you post but I suspect you are initiating an SSL connection from the browser to Apache, where VirtualHosts are configured, and Apache does a revese proxy to your Tomcat.
There is a serious bug in (some versions ?) of IE that sends the 'wrong' host information in an SSL connection (see EDIT below) and confuses the Apache VirtualHosts. In short the server name presented is the one of the reverse DNS resolution of the IP, not the one in the URL.
The workaround is to have one IP address per SSL virtual hosts/server name. Is short, you must end up with something like
1 server name == 1 IP address == 1 certificate == 1 Apache Virtual Host
EDIT
Though the conclusion is correct, the identification of the problem is better described here http://en.wikipedia.org/wiki/Server_Name_Indication