Internet says it's not directly inherited. Which makes sense since it's a mutation during meiosis so the resulting gamete would be XX, XY, X-, or Y-. In order to be inhereted the germ-line cells would all have to be XX or XY in someone with three chromosomes and would be incomplete in someone who had only partial XX or XY and they would likely have pretty severe fertility issues. At least 50% of all first trimester miscarriages are due to chromosomal instability, and being XXY, X, X+, Y, Y+, or XYY all qualifies. For contrast, the number of chromosomally abnormal living people is about .5%. If all the germ line cells of someone who was chromosomally abnormal were also abnormal... that's not great odds for having kids.

Male XYY aren't sterile, but male XXY usually are - but this is because of their testes not working properly, not necessarily what they would produce if they had functional ones.

Most Turner's women are sterile for the same reason - their ovaries just don't work properly. OP lucked out that the ordinary redundancy of the second ovary yielded a functional one and is a perfect example that their gametes are not effected by their own abnormality.