They wibbled, they wobbled, they timed and they wimed.

John Cleese and Eleanor Bron would have appreciated the true exquisiteness of Moffat's arcs. Why can't the viewers?

And in this instance you would be the little girl, the only one who sees through the 'scam' would you?

Lol...

While it's not that hard for the viewer to invent for himself or herself a plausible story as to how the regenerating little girl in NY in 1969 got to be young Mels in Ledworth in the 1990s, it does feels like there should have been an explanation given somewhere in the story.

Trying to be charitable maybe SM felt he had to drop that story element because other elements were more important? Or maybe he wanted to leave some gaps for Big Finish or later showrunners to fill.

At the time it felt to me like Mels popped up out of nowhere without sufficient explanation. She should have been introduced or at least mentioned as Amy's best friend before meeting her as a major plot development in Let's Kill Hitler. She was like the typical 1970s US TV "guest star of the week" who plays a character who was a childhood friend or relative or new or ex girl/boyfriend of one of the series regulars, and who would never be seen or mentioned again.

Think I didn't get was why the doctor failed to rescue Melody as a child and return her to her parents in Ledworth.Like he swore on his life he would do.

He said he knew where she was. So why didn't he just go straight back to the orphanage Florida 1969 and grab her before she got sick and regenerated ?.

I think the Doctor was probably playing the long game.

IIRC, he was already aware this was a part of a plot against him. If he'd intervened in that way that plot would have been deflected, sure, but it would probably not have revealed who the conspirators were. Meaning they'd be able to try another way and he'd have to start again from scratch trying to figure out who he was up against and deal with their threat permanently.

On top of that, being a Timelord, he may also have had an inkling that he had to let it play out to avoid changing River's, and therefore his own time line.

Well The Doctor would have known he would find Melody eventually, he has seen her future self, and knows eventually he will find her and everything will turn out well.