I think one of the misunderstandings going on here, other than misunderstanding how mtDNA is passed on to the next generation (always mother to daughter), is that we don't carry all of our our ancestors DNA, our genes are simply not many enough. Some ancestor DNA is lost from generation to generation, in time this will mean some DNA is gone forever. Scientists try to measure differences by comparing mutations, the differences in DNA samples, between different groups and then excluding a third group from 2 other groups. That's how they could assume Neanderthals share DNA with non-African people but not with Africans. (But they also discovered that Africans share ancestry with some archaic humans that maybe shared ancestry with Neanderthals, so maybe Neanderthals mixed with humans at different times).

To assume the fertility of different "hybrids" is just too much speculation. At several other (later) occasions, there was a clear disparity between the numbers of males and females from different group mixing with other groups, implying some kind of aggression ("war") or male-only migration.