You've gotten some great advise so far.
As for your update: I would either email her back and tell her that since she already shopped for your kids that you and her should both start the gift card exchange NEXT year, and that you'd be sending gifts this year like her, too. That way it will sound like you two have an understanding but will start next year since she's already done her shopping.
You could get her kids the exact same things she has gotten your kids in the past. That way she cant get upset because she did the same for your kids. Just get the barrettes and hair accesories in different colors/styles so it's not that obvious. Or, different kinds of pencils---maybe those mechanical ones, or some colorful pens, or something. This could be taken either way. She "might" get the hint, or, it could just be a coincidence. Either way, she can't get upset because she does the same.
True, you shouldn't punish the kids, but if they are so ungrateful as to not ever thank you I wouldn't worry about it. If they were more grateful that would be different.
Good luck and please give an update. I have relatives like this as well. WE all know it's the thought that counts, but sounds like there is no though put into her "gifts" at all.