You're not going to want to hear it, but you're not going to get the detailed information you're looking for for Rolex or Patek. Both are privately-held companies, and neither publicize the information, so anything out there will be someone's opinion or guess. Maybe close to being right, maybe no close.
You can see how many movements they certify (for Rolex, Patek does not use COSC), and if you average it out across a couple years you may get a ballpark, but just because a movement was certified in 2012 doesn't mean it will be sold in 2012. It may be sold in 2013 or even 2014 depending on which one it is, popularity of the parent models for it, number of models that use it, etc.
For Cartier & Omega you can get the information by digging thru their parent groups financial reports probably. For Omega it's Swatch group and for Cartier it's Richemont. As publicly-traded companies they are required to provide it, but you're going to have to dig thru a bunch of their annual reports to find it probably as they may not report it at the branded level. Contact the parent groups & request copies of their annual financial reports and see if you can peel back the layers. It's not going to be easy as their parent groups have dozens of companies under them.