The new version of 'Parenthood' that's currently struggling on NBC is one of those rare examples where a remake can remain in the same TV dimension as the original. (And neither one is affected by the presence of the original movie which is in its own universe.)
This is because the families, while sharing the same structural dynamic, have different last names; many of the characters have different first names as well.. They are not the same people. In 1989, Ed Begley, Jr. was the de facto head of the Buchman family (just like in the movie). Today, the family in the Toobworld spotlight is named Braverman. (I can't be certain of this, but I wonder if the powers that be wanted to avoid any connection made to Paul and Jamie Buchman of 'Mad About You'.) I'm not sure if the same plots have resurfaced in the new series, recycled from the 1989 version, but that wouldn't matter either. Characters from one show reliving events that happened in other shows happens all the time in Toobworld. The American version of 'The Office' followed the same plots of the British original until they finally ran out and found their own voice. It even happens within the same show - Captain Amos Burke twice had a murder case in which a magician was shot dead while in a coffin that had been at the bottom of a pool. And that crime was even committed on another series, 'Blacke's Magic'. (The reason why Captain Burke couldn't remember the first case when it happened again was because he was in the early stages of Alzheimer's.....)
So the two versions of 'Parenthood' can remain in Earth Prime-Time, in much the same way as all the variants of 'Ugly Betty' can share the same world....