Looks like there no easy way for this. I will suggest a method, but it is upto you make it work.
Create 4 domain names points to your server. womenmysite.com, menmysite.com, women.mastersite.com, men.mastersite.com
Create a proxy from womenmysite.com -> women.mastersite.com
and another proxy from menmysite.com -> men.mastersite.com. For creating a proxy please refer mod_proxy module for apache http server or you can find similar modules for other web servers. If your server behind any other proxy like firewall or load balancer, try to configure these proxies there itself instead of creating one more layer.
you can set cookie domain as .mastersite.com and store sites as men.mastersite.com and women.mastersite.com. Also, you will face some issue with proxy and Magento authentication system. But I think it can be fixed easily.
Here comes the tricky part. You will manually need to write a PHP script that will synchronize the sessions between two websites. you can either implement this using a cross-domain script include or an iframe. For example for menmysite.com.
://womenmysite.com/sync-session?id=some encrypted data
This encrypted data should contain all the cookies sent to menmysite.com.
This script should set the same cookies send to menmysite.com to womenmysite.com.
Also, the similar script should be there for womenmysite.com that links to menmysite.com.
You have to use an invisible iframe too. I have no idea how much tweak required to make this work as I worked with Magento some time ago.