This is a fantastic opportunity to teach your children how to deal with difficult people. Model it for them. Even if this gal is a walking red flag, it should not matter a whit in how you choose to comport yourself and how your children will behave.
From your post, you've already decided that this woman is junk, her kids are 'too old' to have the same fun your child is (my fourteen year old nephew just bragged last night about having made a gingerbread house with his mom, my sister, BTW) and her presents are all wrong.
You are a big girl. You can decide to take Christmas for your family alone this year-- or not. If she's that terrible, I'd have done some strategic planning by now so that I did something with them before or after Christmas day and just kept that day for ourselves.
And yes, you do prep the kids to just say "thank you". This woman might be vile, but she actually remembered to give your kids a gift, and I've heard of worse. Why is she obligated to know your family rule that "no one buys the kids clothes"?
Your brother is a big boy. Let him deal with her as best he can. I think you are feeling sorrier for him than he likely really needs. He *chose* to leave his marriage. He *chose* to be with someone who has no plans of having any more children. I think you are so busy hating this woman that you aren't letting him be responsible for his own choices. In the mean time, teach your kids that this isn't all about *them*. Either do the family gig graciously or politely make another plan.
Believe me, I have sat through some holidays with some truly horrible people and all I had to do was be polite. It isn't that hard. ("more wine, please?" "Oh, I need to go ask Aunt Mabel about her recipe... excuse me a minute"....)One and Done had some good "cut'em off at the pass" suggestions for responses to gauche, 'gold-digger' questions. And remember, learning how to deal with difficult people and situations is a great gift to give our children-- they will need these skills lifelong. I understand you want to vent, but it sounds like you might need to be a bit more proactive in your holiday planning, because this woman isn't going away anytime soon.