I love some of the suggestions you already have! Encouraging lessons instead of items, having the gifts come to you to parcel out slowly as rewards, etc ... those are all good ideas.
I think the one thing most likely to get your mother to stop buying so much would be spending a lot of time with your children in your home. Basically, she needs to trip over the toys, try to manage the clutter, etc., to realize that it really IS too much. The reason I suggest that is because my mother is very cautious shopping for our kids simply because after caring for them one day a week in our home she concluded that they had way too much stuff and couldn't even enjoy it all properly, and decided to shop for underprivileged kids instead.
Still, it may or may not work. We had a nanny that loved to pick things up for my son at Goodwill, etc., and it drove me nuts. I wasn't paying her to fill my house with stuff! Yet, long run, we dealt with it, because it made her so happy to give my child gifts.
Whatever you do, please be very careful in how harsh you are towards your mom. I have an aunt and cousin who no longer speak because of a battle over gifts for the kids. NO amount of clutter and unwanted toy volume warrants that kind of fracture. Your children aren't likely to get spoiled from too much stuff, especially if it isn't stuff they have specifically asked for, although it is likely to hinder their sense of responsibility and care for their things. But your children WILL suffer if you become aliented with your mom over this issue. Try not to fight, but do try to let her really see and understand this through your eyes.
Best of luck. Funny how affluence brings it's own issues, isn't it?