Nowit, you have a week of this and sounds like DH is being classically DH about it.
You need to tell her that you are really very, very grateful for everything she does for you as a family...
BUT that this close to christmas really there can be no purchases as she could be doubling up and unwittingly stomping all over someone else's gifts. That there really is absolutely no deviation from this rule, or it just gets silly and you all end up with grabby spoiled children.
Then there is the issue of favoritism, that it's imperative that all the DC are treated absolutely equally, at the same time. This can be gently raised and discussed, but it MUST be tackled and stopped immediately.
Say that you appreciate this is hard, but that you and your DH have managed to work it to a fine art and that you are more than happy to help her be included in this process.
Tell her that if she DOES want to be the one to buy a winter coat, that is fine, but that in future you will be organising the trip to buy one, for all the DC so that no-one feels left out, as they do now. Get your diaries out and plan a trip next year, for birthdays, easter, christmas, whenever.
Remind her that in time it'll be so much easier for the DC to understand what is going on,but for now they are too young and it could spoil them,or cause unnecessary upset.
You have the January Sales, so this is the time for her to kit out the DC, not before.
Forget getting DH to resolve this, he won't, this is a woman's role, a woman's issue, to kit out the DC and plan gifts etc. Giggle with her that you have asked H to broach this with her, but you know how that goes...employ some eyerolling, shoulder shrugging and a liberal sprinkling on 'Men!'
You can work this so that it is a great arrangement, you can teach her to be a great and fair GM, and you will in time enjoy her visits.
If you leave this issue to fester, or ask H to fix it, you will end up pretty much murderous by the middle of this week.
Tackle it now, get her on your side and work together, you both want the best for your DC so guide her. You'll still need to be firm, but create the dialogue that you will need to get this working.
It's down to you, you can do this!