I don't believe heaves is hereditary, but have not done much research on this.
It really sounds like this mare is having an allergic reaction, and it is affects her breathing. Unless she shows signs of it at different times like the seasonal changes, after a good hard run or play with other horses, etc. than I would question if it is actually heaves. Has this mare been diagnosed by a vet?
Heaves usually get worse as they age. If taken care of properly they can live a relatively decent life. But you must know that they are best left outside, not in enclosed stalls. Their feed should be wet down. Try to keep them out of dusty areas. And since she has a reaction to alfalfa, it would be best if she is not kept in the same barn as the alfalfa hay. She would not be able to eat with your other horses either since you feed them alfalfa.
I have had a horse with heaves and it isn't fun when they are having a bad episode. The medicine can be really expensive also.
Then when it gets really bad you have to make the decision when you need to stop their suffering.
Good luck with your decision.