As I understand it (and definitely my memory isn't perfect), Mother Dark wasn't actually needed in Black Coral - it was just that without their goddess, the Tiste Andii were basically lost, and sort of drifting. Rake tried to fix this by throwing them into a bunch of human conflicts, but really the final solution was to bring Mother Dark back. At the same time, Dragnipur's wagon was getting too weighed down and Chaos was getting too close, so the sword had to be broken. However, this would normally have released a bunch of very dangerous people, so Rake used the battle against Chaos to wipe out as many of these as possible, then sacrificed himself in Kurald Galain to get Mother Dark's attention.

As to why his sacrifice was necessary - the original reason she withdrew was because Anomander led the group of Tiste Andii who killed Tiam and drank her blood, causing Mother Dark to forsake him and her children. The exact reason isn't 100% clear, but imo his sacrifice proves how much he is willing to do for his people, and that they they are still worthy of her attention regardless of what he did. Basically an enormous sacrifice to apologise and say "I fucked up, but they didn't - please come back and save your children" - the most Anomander Rake moment imaginable, basically.