Saccharine, contrived, and overly long.
On one level, this story is an attempt to make the canonical fact that Sparkler is Dinky's sister and that Derpy is canonically a relatively young mare conform to the fanon that Dinky is Derpy's daughter. There's nothing inherently wrong with that, but the fact remains that this story is saccharine, contrived, and overly long.
It is contrived in the sense that all the dramatic tension comes from the fact that Sparkler suspects that Derpy doesn't really love her and only adopted her to have a domestic servant. The problem is that Sparkler is clearly nearly a legal adult at the time of her adoption: she already has her cutie mark, and is no longer obliged to attend school at the orphanage. There is no way any orphanage is going to allow a nearly grown child to be adopted by a prospective parent without the prospective parent and adoptee talking to each other at great length and both agreeing to the adoption. In this story, Sparkler just wakes up and is simply told that she is being adopted by Derpy. So a lot of Sparkler's issues and concerns about why Derpy wants to adopt her would have been addressed long before the adoption was ever finalized, and Sparkler would only have agreed to the adoption if she were satisfied that she would be happy with Derpy.
Secondly, the dramatic tension only escalates to any kind of serious dramatic crisis because Sparkler interprets everything
Derpy says or does in the absolutely worst
possible light. Anyone who behaves the way Sparkler does in this story clearly has deep-seated trust issues that could never be resolved with a letter and a hug.
That's why the story is saccharine. The simple fact is that Sparkler's behavior in this story, prior to the letter, is abominable. That what she does is resolved with a nothing more than a hug and a few tears is too easy, and too overly sweet.
That is why story is too long. A realistic tale about an older adopted child being integrated into a family could justifiably go on much longer, but, again, the dramatic tension in this story builds off of trivial incidents, and the dramatic crisis in this story is resolved absurdly easily. Given all that, the story ought to have been much shorter.