@TenaciousDreamer2nd
That was more of a sub-plot conflict then an “arc.”
It wasn’t really all for nothing, as Splinter did reunite with her eventually, had some touching moments with her, and she learned the Shredder wasn’t her real father, and she befriended the turtles, became their ally, and such.
TVTropes honestly oversimplifies things, or doesn’t note everything.
TMNT 2012 isn’t perfect, but I actually think it’s one of the better TMNT shows. (I even prefer it over the new one.) So it’s a shame you feel that way.
It has humor without being as goofy as the classic cartoon, it has some rather dark/edgy moments without taking itself too seriously like the 2003 series sometimes did, and it combined many different characters, and concepts from all the past canons, without pandering, or trying to be too original.