Really? Why do you consider that to be so? William is the one with Diana's genes. I haven't seen any evidence that Catherine has any of the instability that Diana demonstrated. Catherine seems to have a perfectly sound family background with close and loving relationships with her parents and siblings.
I in no way meant to imply that Catherine has any of Diana's instability, although I can see how what I said could be construed in such a way.
My understanding of Diana is such: she was an unstable woman prone to depression and jealousy, from a broken family. She longed for love and failed to find it in her marriage - either because it wasn't there or because she failed to recognize it in the form that it took. She really seems to have construed her relationship with Charles as one of emotional abuse and neglect (although, once again, this can be seen as her interpretation of it, not what it actually was) and sought the love and protection that she was failing to receive in her marriage elsewhere - from her son. Because of Diana's understanding of her relationship and the way she felt that she was abused/neglected she forced her son into a position where he had to act as her protector. This is more typical of relationships between mothers and sons than fathers and daughters (or even fathers/sons or mothers/daughters), thus if it's likely to happen again it's more likely to happen between Catherine and a son than William and a daughter - not because of genetics but because of gender relations.
What's more is that while William has the genetics of Diana (although he has not, to the best of my knowledge displayed the instability) and the troublesome childhood, neither of which his wife has displayed, there are still a lot of similarities between Diana and Catherine simply owing to their position in life. William may be from a broken home, but he belongs to a family that is tight-knit and in which he is heavily supported - and belongs to a world that isn't exactly well known for letting people in. Diana had the problem of being an interloper within the BRF who struggled for acceptance, Catherine is likewise an interloper - although all appearances show that the BRF has learned from the folly that was the Charles/Diana relationship and is working more to accept newcomers (Catherine, Sophie, etc) than they had previously. Regardless, though, Catherine faces more public scrutiny as the wife of the heir than the heir himself and in a way is in a position that is more challenging than William's. As such, were this marriage to crumble like Diana/Charles, or if relations between them and their children were to take similar dynamics as the overall Wales' family dynamic, I would more expect William to fill the role of Charles and Catherine to fill the role of Diana than the other way around. It's in no way meant to be a comment on either of them and their own instability, so much as one on their roles and positions.
All that aside, Catherine's own background and the history of the relationship to date (plus the lesson that the BRF surely learnt from Diana), there is every indication that this relationship is not going to end up like that. The sins of the father do not have to be the sins of the son, so to speak.