I agree with all of the suggestions listed after my initial response.

Staying in a harmful, neglectful, and abusive relationship does no good for either party, including the children involved. The children witness these pains, or at least suspect something is going on. The children often learn from the adults' behaviors and choices in life. Staying sends a message to the children that it's okay for people to be cheated on, for gender roles to be okay and acceptable (e.g., it's okay for men to cheat on women, as long as the women are silent, soft-spoken, and obedient to their male partners), and for lying, rumors, and a lack of boundaries to be tolerated or accepted - at the expense of a miserable relationship that affects all in the immediate household.

Conversely, setting boundaries, having some self-respect to leave abuse, and prioritizing children's health through examples of setting boundaries and leaving when abuse happens will be healthier for everyone involved. The abuser might not like it, and the breakup might be painful for all, but those things are necessary for both individual and widespread change in these areas. It's not okay for popular people to get away with cheating and lying, and it's not okay for women to have to bow down to the man, and it's not okay for people to spread rumors instead of going to the source and confronting what they saw (if they truly care about the partner/woman who is being cheated on), and it's not okay for children to have to suffer from constant fights and seeing the victim constantly hurt and taking all the abuse without leaving (even if it is emotional abuse, and not physical), because that, too, affects development. Children's brains form all the way to age 25. Adolescents, too, need parents to be good role models. When one of the parents fail, another guardian can demonstrate what is right by setting an example. It's a sticky situation here, but doing the right thing will help everyone.

Wanting only feel-good responses in cases like this is unrealistic because (a) one or more people are constantly being abused and neglected, and (b) a child is involved. Unfortunately, you can't tell a victim that it's okay to stay in an abusive, harmful relationship and then just comfort the victim when the victim does, in fact, have choices that are healthier. That would be enabling and condoning such behaviors to continue.