If it’s the story I’m thinking of, the mother was using the fluffy as a surrogate for her own dead child and deliberately kept it isolated from everything so it wouldn’t realise it was a fluffy. That plan failed and the woman killed the fluffy, forcing her to start again with a new one.
There’s two other series that I know of, both with a single mother using a fluffy as a surrogate for a lost child. One is a sadbox and the human sister loves the fluffy as if it was an younger sister; the other is a revenge story where the human daughter uses the help of a local fluffy expert she befriended, to turn the fluffy into a spoilt brat, causing the mother to prove that she’s unfit to have custody of her so she can move in with her father.
Edit: First story is Little Tim by Rescue_9.
Edit: Second story is Elenore (chapter 1 and chapter 2) by Julie
Edit: Third story is Tricky Treats and Baby, both by ChungusMyBungus.