The Warden presence in DA2 may have been due to the matters addressed in Legacy - the documents, the presence of Nathaniel, etc, all could point to the Wardens seeking information or artifacts from what was beneath Kirkwall and the surrounding areas. Which in turn could point to the further research on the Blight. Maybe the Warden agenda was to pick up where the Band of Three left off.
As for DA3 - if indeed we will be traveling somewhere decidedly more French, I think we'll see more of Orlais' involvement with the Order. Not only is there a stronghold there (including an
abandoned one, according to Asunder - **spoilers within that link), but the Empress was working with Ferelden to combat the Blight. Darkspawn are still a threat, albeit one that is a low rumble. Orlais may be supporting the Wardens more than ever before, and while political ties are eschewed by the Order, they may be in need of funding and arms, and may be accepting it on behalf of the perceived greater good of preventing more blights. But if the taint can be mastered as opposed to vanquished (perhaps mastery is easier than annihilation of it), then that could be utilized as a weapon. The empire/group that holds the ability to unleash hordes of a walking plague of sorts would be an entity with incredible sway and power.
Perhaps there is a schism within the Order itself, parallel to the mages and templars - some wish to stop the darkspawn threat altogether, some wish to manipulate it. This is somewhat addressed in the varying viewpoints regarding the Architect in
The Calling. Maybe that underlying divide is what is fueling the Order's actions now.