Don't actually understand what you are asking?
I gather from the information given above that your daughter had some deposits of calculus around her lower anterior teeth (very common).
Presumably this calculus would have associated coating of plauqe/biofilm (always does), this very often leads to gingival erythema and can increase the friability of the tissue on occasion this tissue can be necrotic and require removal.
Especillay in the conditions known as AUG (Acute Ulcerative Gingivitis) and AUP (Acute Ulcerative Periodontitis),
Erythematous friable tissues can bleed spontaneously and given that there is an excellent blood supply to the oral soft tissues and keratinised gingivae it is very common to get bleeding (around the 'gum margin') in the presence of gingivitis when toothbrushing and therefore it is no surprise that there was bleeding following removal of calculus deposits (afterall this is technically a form of trauma to the tissues).
Presumably the dentist has removed some necrotic gingival tissue and placed a protective sedative dressing while the area granulates/heals.
So if your question was 'Is it normal for gums to bleed following dental scaling?' then the answer would be yes (especially if there was a pre-existing gingivitis/erythema/swelling/large amounts of plaque and/or calculus)
And if you are also asking 'Is it normal to remove swollen gum?' then the answer would be that this is not overly common, however if the tissue was particularly necrotic and therefore unlikley to heal then it was possiby appropriate to remove it and allow granulation.
Its hard to answer accurately without more information and without knowing exactly what you are asking.