I would start by not judging this as an overreaction which implies that her response should be different and is incorrect. Her reaction is her reaction. The only thing you are in control of is your response to her reaction. Everyone here is speculating as to the reasons behind her reaction -- these are guesses based on insufficient information.
She is upset about the text -- and that is primarily all that matters.
My advice is to listen to your wife. Tell her that you understand that she is upset about it (you don't need to understand why, you don't need to make a judgment about whether she should or shouldn't be upset, and you don't need to justify the other lady's intent). Tell her that the most important thing to you is that she (your wife) is not uncomfortable about the situation and you are willing to do whatever will help her to not be upset about it. If she asks that you cut off or limit contact with the woman tell her that you will do that because your relationship with your wife is far more important to you than sustaining an acquaintanceship with this woman and her son.
It is possible after this conversation that your wife will relax and perhaps find a solution that makes her comfortable and maybe doesn't require you to cut off all contact (probably an uncomfortable thing for you to do). The bottom line is -- acknowledge that she feels upset by it and that her discomfort matters to you.
