I'm not a big fan of the term "broken home." It reeks of melodrama. "The poor child! She comes from a broken home! How ghastly!" I've also never really understood the phrase, "Staying together for the kids." When I hear about couples doggedly and unhappily sticking it out for this reason, or a parent being torn apart about what a divorce will "do to the children," I generally just want to shake everyone involved and shout, "What do you think living in a home with a tense, unhappy, loveless marriage is going to do to them??" Kids are pretty astute. They know when something's up. They know when mom and dad are secretly seething at each other over the dinner table, and (spoiler alert) they can definitely hear you when you fight behind closed doors.
I guess I'm just saying don't martyr yourself in an unhappy marriage for the sake of your children. If you decide to end it, and do so while ensuring your kids know you both love them and will always be there for them, odds are your kids are going to be a-okay. Yeah, they might shed a few tears initially and they'll definitely be an adjustment period, but they'll hardly be ruined for life (unless you totally screw it up by being petty and immature and putting them in the middle, in which case you're probably totally screwing them up anyway).
Would it have been nice if my parents had gotten along and stayed together and we had all been one big, happy family? Of course. But that would also by definition mean that my parents would have been two entirely different people than who they actually were. And as an adult who can look back and remember their dysfunctional, miserable dynamic, I would never wish it on either of them for my sake.
Maybe that's a key to growing up: the realization that your parents are people outside of just being your parents. They have whole entire emotional inner lives that we are pretty selfishly unaware of as kids (and that's the way it should be). If my parents had waited to split when us kids had all left the nest, I'd like to think I'd tow the line of, "You let yourself be miserable for 20 years for us? Jeeze guys, we would have understood!"
Bottom line, your kids love you, and if they grow up to be empathetic people capable of complex thought, they'll understand. And to be totally honest, there were plenty of times when my parents did put us in the middle and did make us little mediators and did do a lot of the things that all those fancy divorce books now say not to do, but guess what? As an adult, I still understand! They were hurting. They had never ended a marriage before. They were just trying their best. And I still love them (and you can be sure I still call home to tell them when their favorite movies are on TV or when I'm wondering if Raid is poisonous to cats).
So divorce if that's what you need to do. The kids will be fine as long as you continue to be loving parents who they know they can always depend on. And if you're not that, then yeah, expect them to have issues -- whether you stay married or not.