How can she tell her non-Muslim mother that her husband is going to take a second wife?

what is the best way to tell my non muslim mother, who is very critical of islam, that my husband is about to take on another wife?

Praise be to Allaah.
There is nothing wrong with you happening to mention to your mother whilst you are talking to her that your husband is thinking of taking a second wife, and telling her that he has valid reasons for doing so, such as not having any children from you, or that he is not satisfied with one wife, and so on. That will be like an introduction for her if she knows. But do not tell her about the matter now, less that open the door to problems for you that you can do without. If she finds out about that in the future, then you can explain to her, one way or another, that Islam is the religion of justice and does not approve of injustice on anyone’s part, and that in a plural marriage there are many great benefits which the countries which claim to be civilized cannot attain. (See question no. 12528). Even if she is not convinced at first, she will become convinced as the days and years go by. But you should not express too many objections about this matter in front of her, because by doing so you will provoke her to criticize Islam. Rather you have to show her that you accept this and approve of it, and show her that it is not affecting your relationship with your husband.