I'd cut granny some slack here in terms of intentions; I'm betting that there is a class migration involved in this scenario -- that the OP is better off than her parents were when she was in school. Granny probably remembers feeling really anguished that she didn't have the resources to spare the OP the teasing of classmates back then, and now she wants to make up for it. (There may also be some frugality issues as well.)
My question would be, is granny really making fun of the children's clothing, or questioning their choices, perhaps in a sort of joking way that she may think is lower-key? ("That dress is kind of baggy, don't you think? Does anyone else at school like that style?)
I would say that the most important issue would be; are the kids upset with Grandma over this situation, or is the OP the only one who is bothered by this? If the kids are not upset with granny, then the issue is not what the kids are wearing, but boundaries between the OP and her mom.
If the girl likes her CP backpack and doesn't care if anyone teases her (IF anyone teases her), then she should keep using it. Thank Granny nicely and put the PB backpack at the back of the closet; maybe DD will prefer it next year.
It's really not unusual for someone two generations removed to think that an outfit that a kid chooses lacks style. My mother was 48 years older than me, and it took years for her to accept that a post-pubescent teenage girl not wearing a girdle to school wasn't indecent -- and we won't even discuss her opinion of women wearing jeans.

In such cases, I find the best thing to do is usually to chalk it up to an uncrossable generational divide and try to let it slide off your back. Yeah, it doesn't reflect well on Grandma, but if she has good intentions, then perhaps this battle just isn't really worth fighting.