Even if your children actually have that money - your fiduciary duty is to them, not to yourself. You cannot gift away money they own for your own purposes. They have to want to gift it away, since it belongs to them. I doubt they do, or they should.
Since you have to have their best interests in mind - you shouldn't allow them gift away such amounts even if they're willing to. Doing otherwise will be a criminal act on your behalf (embezzlement/breach of fiduciary duty).
Do talk to an attorney of course, since I'm not. But that is my understanding of things.
If your kids don't actually have the money, then they can obviously not gift it, so claiming that they did would be a tax fraud.