I agree with Jimmy Fix-It, there's a problem with the drapery mechanism that is making it drag, and someone rather than finessing or fixing it, is just applying excessive force even after the first incident. You might want to have a word with that person; better yet, task them with the drywall repair so they can develop a healthy appreciation of just how fragile the stuff is.
Now as far as a longer-term repair. I was surprised you'd have a problem, because all my windows are framed in wooden trim right where the curtain rods need to go. So I'm going into real wood.
I would find the studs, mark em with masking tape or something non-marking, then go one of two ways.
Attach the curtain rod to the studs directly with longer screws. It's not that you need 1-5/8" screws to hold a curtain rod, but you do when the first 5/8" is chalk. If that position is too awkward, then...
Figure out where to put a 1x4 so it'll bridge across studs in all the right places, and not have much of a cantilever where you attach the curtain rod. Let's say you want to attach the curtain rod 2" from the end. If it hits a stud 4" from the end, that's fine. If it hits the stud 12" from the end, that's a problem, because you'll have 10" of cantilever and it'll bend and break. In that case, extend the wood 3 more inches so its end is on a stud.
Then I'd trim out the 1x4 with a router to give it a rounded appearance, i.e. a 3/16" radius to help it look professional/built-in if that makes sense. Sand it smooth and prep it for prime and paint.
Then bolt it to the studs with countersunk screws (predrill so you don't crack the wood, and countersink so the screws are flush).
Then prime it and paint it to match the room so it looks built-in. Which it is now.
Then hang the curtain rods off the 1x4.
If you want max strength, go oak.