Hello.
There are several different ways to solve your task. It depends on used frameworks, on database structure, on some server permissions. There are 2 main subtasks
1) auto registering user in second service. Both frameworks to be researched: how many tables are modified by new user adding. If only 1 table modified and if your server allows to use MySQL triggers then the best way is to use trggers on insert, update and delete. Triggers will do the same in other database. No site code to be changed in this case. But if more than 1 table modified then the best way is to find some function to create user in second framework and use this function.
2) auto login and logout in second framework. Again at first research needed: what cookie and what session variables set frameworks on login? Are session variables and cookies accessible from second framework? They should be due to residing on the same server and domain. So small adding to autentification process to be added: analyze existent cookie also.
I did samejob before, for example using phpBB phorum inside vTiger CRM. But this project is internal and I can't show it.
Do you use some standard frameworks for web-mail and for dating site? What are they? Do you use shared hosting or some VPS? In second case it will be possible to mpdify some sever preferences and it might help to solve the task more quickly.