What do my kids need to know about all this genome stuff?

Depends on age. Below the age of 7-8 yrs, kids are unlikely to process the information any deeper than they do the tooth fairy. 8-16 are straight forward & basic, after 15 or so they are more adult in sorting issues out. That said, i see little relevance to their daily life in bringing up the subject at all.As they approach adulthood & issues of parenting & inheritance arise, you have good reason to review it.