You have an opening for a promotion that you have to fill and have two possible candidates: Linda and Darnell. They are both fairly equal in terms of production, yet you are leaning towards Darnell because the way in which Linda talks about her colleagues disturbs you.
For example, you overhear the following conversation between Linda and a coworker.
"Don't ask Darnell to do it!" Linda complains. "No, we dare not ask Darnell. He's such a weenie about his kids' soccer, his kids' dance recital, his kids' story hour."
She trails off, saying "blah-blah-blah" while making making a babbling mouth gesture with one hand.
Discussion
There are two issues here. The first is that Linda is showing a lack of respect for Darnell's life situation. You need to talk to Linda and explain that you are trying to foster an environment of respect. Darnell obviously cares a great deal for and is proud of his family, which is very commendable. Explain that you feel it is inappropriate and disrespectful for her to talk about her coworker in such a manner, especially to you. Make it clear that having a family is not a reason to discount someone for a promotion as family values are very important and if Darnell is chosen for the promotion it would be because you believe he could handle the responsibility while balancing his children's activities.
The second issue involves Darnell. You need to let Darnell know that you are considering him for a promotion and see if it is something he would be interested in. If the position requires more of a time commitment and may take him away from his family you should be upfront about it, as he may not be interested. On the other hand, he might be very excited for the opportunity and want to take on the challenge. He may even have some great new ideas for how he can maintain a good work life balance with the new responsibilities of the position.