First King Cold was the strongest, that much is mentioned in the series. It just didnt matter, at all, the gap between them and trunks was too much to be relevant.
Second There were quite a few sayans that survived if im not mistaken, Turles ( another Gokus Brother)
Also meet vegeta brother Tarbles....
Third how the hell would Broly unite anyone? It will defeat the porpuse of the character... because He didnt control his power, his power controled him, and thus he was slave to its nature. Destruction, and conflict and instint, it was what drived Broly, and his peculier hatred of kakarot.
Besides wasnt that what Brolys father wanted to do from the begining to conquer and rule by using broly? only to get killed by it....
The last thing i seen from dragon ball was that battle of gods movie, it was ok enough, if you are looking at some laughs, and light entertaiment. If you can overlook the already expected plot devices... at least Bills was interesting entertaining character.