I wouldn't bother fooling with the sleeves and have your daughter return the jacket if she is not that crazy about the jacket to begin with.

Well, I would try if she really doesn't want to return it...I'd do like you say and carefully re-pin taking in that extra fabric...if you are careful you should get an ark of extra fabric (seeing as you say it is gathered)..you go slow and take away as much of the fabric as you can without changing the line of the sleeve. It can be done, my girlfriend had wonderful sleevecaps and she showed me how she achieved them...OK she didn't have the edges of the two fabric meeting (jacket body and sleeve )but it eliminated the excess bunched fabric.

If you decide to tackle this, you can take in the extra fabric with darts - beats trying to ease in that much fabric. Or you could run a seam down the top of the sleeve - since you don't want to take in more fullness down around the elbow, the seam could be miniscule when you get out of the sleeve-cap.

How much does she like the jacket? Because it will be a fair amount of work, and if there are other features she doesn't like, she may as well take it back.

However...I generally "slash and spread" to go from a plain sleeve to a gathered one. Once the sleeve is removed, you could reverse the process to make a new sleeve "pattern," and cut the new sleeve from the old. Measure the seam of the jacket armscye, and the new sleeve should be...ummmm, 1/4 inch more on the front half, 3/8 inch more on the back half. You ease sleeves in when you set them, right?

A pattern dfrom your local library would be helpful.