If it were me, I'd send them back or return them to the stores they came from, so she will get the money back. This will teach your kids financial responsibility. If you keep all of that stuff, your kids will have an unrealistic perspective on gift-giving, and on spending.
Of course, you could pick out a few items per kid or allow them to pick, first.
That's what I'd do. It might feel tempting right now to keep it (I don't know; you are understandably angry about what she's doing to herself and the example she's setting), but the more financial mess she creates for herself now, the more you will be asked to help later (especially because you accepted such gifts!). Another issue, though I hate to bring it up, is, what will your legal responsibility be in the event of her passing? Doesn't family have to pay the debts of the departed?
She sounds a little like my mom, who, after years of impoverished single motherhood, went nuts on spending spree after spending spree, lived too close to the edge and has been paying for it ever since. She still buys way too much and then without apology announces that we won't be getting Christmas presents because "they can't afford gifts." I think that what has been happening is, she got into a habit of overindulgence after spending so long working so hard and feeling want and living only to care for her kids. But instead of spending so much for so long, she could enjoy living her life as a free woman without so many responsibilities, and she really does that, too. Maybe this is what is helping her to reign it in a little, spending-wise - she's involved in local politics, her garden, some social groups. Maybe your mom could use a little encouragement in getting out and finding what is truly meaningful to her to take the place of so much spending.
Maybe do some legwork to get her into therapy. Give her some numbers to call of places near where she lives. Be very positive and encouraging. Tell her that there are ways she can direct her energies and feel that she is indulging without all of the stress that she is also certainly feeling over it.
I have to admit, I like buying stuff online, too. It's so fun when a package arrives in the mail. One way that this is turning out to be okay is, I'm starting a work-at-home business where, handily enough, I have to buy supplies to turn into products! Fun stuff, too, colorful fabrics that I'll be sewing into useful stuff that will make me profits. Maybe your mom could consider doing something like that (doesn't have to be online, of course, if she doesn't want to deal with a website; she could sell products to local stores or a farmer's market or such places). This way she can start to pay off her debts, too!
L.