I am not sure that your algorithm will generate more secure passwords. I think it is likely that the passwords will be less secure because you are ruling out large segments of the "password name space".

If passwords can have a max of:
- 2 upper case letters (AB) in a row...
- 2 lower case letters (xy) in a row...
- 2 non [A-Za-z0-9] letters in a row...
Geez...

This will be an intrinsically insecure system because the requirements are so extreme that the users will write the passwords down on paper (they are too weird to remember). Or they will come up with simple algorithms 1QaZ2WsX or whatever that easy for a program to guess.

I would talk with your security folks. I think your proposed scheme has some serious flaws in practice.

A password like: my2ndDogCamero is a pretty hard thing to guess, but might be pretty easy for me to remember - so easy that I don't have to write it down on a "sticky" in an office drawer. Maybe Camero is really my first car instead of my second dog...whatever..