You say she'll just be shooting skeet with you. That takes out short barrels which are not permitted at some clubs. There are competing issues with weight. A small frame gun is easier to hold up and swing. It does lack the weight that soaks up recoil though.
Not sure why your instructor was recommending 12ga. Many skeet shooters would argue that 28ga is no handicap at all for skeet. 3/4 oz loads at a moderate 1200fps are very soft even with a light weight gun - and
if you reload are cheaper than 12ga. 28ga pretty much requires reloading as factory is pretty pricey. If you start her right, this will most assuredly not be her last gun.
Though we may disagree on much, I think we'd all agree it's a good idea to try a variety before buying. To that end, it might help to fill out your profile so we know where you live and shoot. I shoot mostly at Silver Willow North of Calgary and I have a variety of 12ga and 28ga, gas semi, pump and O/U - most of them with shortened LOP that she'd be more than welcome to try. (Most shooters are more than happy to show their guns and to help a new shooter on their journey.)
Best of luck to you both.