Mauriherb. You raise a very good point. It really depends on the relationship between them. If it is like your relationship with your DiL then showing unbiased friendship might be a most natural thing. The problem arises when it becomes "two against one", which is very hard to avoid when one party, here the woman, wants to leave and the other wants her to stay. If his mum joins him to talk to the one wanting to leave, she cannot help but feel she is on her own against two. It needs a very strong relationship between MiL and DiL and very careful handling. So much depends on all the circumstances surrounding the situation.
We do not know how long she has been thinking of leaving. It might have been going on for a long time. Possibly something has happened to her, somebody talking to her maybe, that has made her appraise her life and situation and led her to decide she does not want to go on as she is, in this relationship for the rest of her life. Sometimes we know deep down that things are not right but we think we need to soldier on and it will get better, then something happens or several things happen to enable us to see ourselves and our lives differently and we know we need to make changes. However kind and tactful and caring this man's mother is to the partner who wants to leave, she will inevitably feel that his mother and he are upset with her and are trying to persuade her to stay. She will possibly become more entrenched in her decision as a result.
I do think it wisest for his mother to keep out of it and not try to talk to both of them. Many things go on in a relationship that a person would not want to discuss with their Partner's parent, however close they felt to them. This girl knows how much her MiL loves her son, she might feel uncomfortable about talking to her at the moment. I doubt if she is feeling on top of the world herself. It probably took a lot of courage to take this step.