Fighting in front of the kids
Okay, so maybe I'm alone in this but I think you SHOULD fight in front of your kids. But you should fight the way you want them to fight. That means don't lose your temper, think carefully about the words you use, think about the issue from both points of view, and talk it through until there is an acceptable solution for both parties involved.
My point is that children learn how to deal with other people from our example. They WILL disagree with someone at some point in their lives. If we hide our disagreements from them they'll have no reference for how to deal with these situations. Not only with this most likely lead to a lot of physical confrontations and tantrums, it will give them an unrealistic view of how the world works. I mean if they never see you fight they could think that means there shouldn't be any conflict in a good relationship. What if you son or daughter has met "the one" but throws it away because they fought from time to time? Or worse, they've only seen you hide your feelings, act passive aggressively, and give up on communication so they do the same. That's not healthy.
Of course, setting a bad example is worse then no example. If you or your SO can't fight maturely then by all means wait until the kids go to bed or duke it out in your bedroom where they can't hear. But if you can manage it I would suggest showing your kids how you think they should handle conflict.
I think you do want to teach them how to handle conflict.