My mother-in-law is unbearable. She has called my children (ages 6, 4, and 7 months) names in front of them, starting when they were under 1 year old. Names such as liars, wusses, divas, miserable, and crybabies. If one of the kids is hurt and we comfort them, she angrily tells us to "stop rewarding their bad behavior." She gives my husband abuse and criticizes me every time he calls his parents. He hangs up feeling awful. We can't predict what she will take issue with each time. We are very close to cutting off ties.
Fortunately, it sounds as though you and your husband are pretty much in agreement about the nature of the problem, but perplexed as to where to start. My major recommendation is that you and your husband work out a team approach to his mother's hostile behavior.
You might decide to have a calm, friendly, grown-up meeting with his mother to discuss what is concerning you both. Explain that you are both working on "being respectful" with your children and that you need her to join you. Insist that everyone in the family use good manners and avoid name-calling. State that you want her to join you in family therapy or state that you are going to limit family communications to ones in public places, like restaurants where people do not call names or insult one another. These are not your only options but simply examples of ways that couples can set limits with hostile relatives.
Make sure to say that you do not want to cut off ties with her, and that you both value the relationship with her as well as your children's relationship with her. But it may happen that cutting off ties proves to be the only solution. Before you get to that point, however, brainstorm less drastic interventions that might lead to gradual improvements.
The key to success is that the two of you thoroughly discuss the problems that she poses to your household and form a unified front to deal with her. This is not going to be one conversation for you and your husband but many conversations, and consulting with an outside expert (such as a family therapist or mental health professional) might help you both arrive at the most effective approach. Don't rush the process.