BUT, my theory of Claire being her daughter isn't just based on that
LOOK
When Claire accidentally opened Alice's door, Miss Thavel looked aggravated, and Miss Circle was simply like "oh crap 😀". BUT, look at Miss Bloomie's reaction
She looks upset?
But, a reminder that Miss Bloomie was also the only teacher that chased Claire around WITHOUT a smile
She DID cut Claire's leg to stop her from getting away, but nowhere does she look happy about it
HMMMMM... 🤔🤔
EDIT:
Also, notice the shape of Claire's eyes? It's just like the teachers'. It does appear that Miss Bloomie can open her eyes wider to be fully circular, and while we don't see Claire do that, still
Not to mention, they both have bows in their hair. This isn't indefinite proof Miss Bloomie's Claire's mom, but they do have a VERY similar wardrobe