You guys have a couple issues. First of all, your windows and window trim are out PAST the stucco. Its creating a natural edge for water to funnel back in behind the stucco, in around the windows. You also have a flat sill surface at the bottom of each window trim that allowing water to sit on, or run back into the jamb area.
If you can see water on the outside (which I can) you can bet you have water inside the wall.
Secondly, I do not see any kickouts at your roof/wall intersections. Water is funneling in there, down behind the stucco.
I have installed stucco for 30 years, and I'm also a licensed engineer and licensed stucco inspector here in SC.
Caulking is not going to solve your issue.