Speaking from experience, this is how my relationship started off with my mother-in-law, and it never helped to sweep things under the rug.
I used to let it slide, which just gave her permission to continue talking about me/my family, and in turn my not wanting to confront (
that doesn’t mean you have to yell or be rude) the problem kept me from wanting to get close to her- I have always kept her at an arms distance from the moment I found out that she talked
about me rather than
to me. At first I did it because I was hurt; over time my decision hasn’t changed simply because “you can’t miss what you didn’t have” and I was never close with her anyway; I also realized over time that I don’t want to be part of gossip, and being close to her would open me up to (1) hearing about other people in a way I don’t want to, and (2) it could potentially give her more fuel for her to gossip about me/my family to other people even more- who wants that?
If I could do it over again, I would stop her from the get-go and address the problems she aired to other people about me, my husband marrying me, and our children- and she has said and done some pretty hurtful things in the past directed at me. I am fine with my relationship with her now because I’ve stood up for myself and have re-grown my backbone, but I regret not sticking up for myself in the beginning- and essentially my family, and in a way giving her the “OK” to keep up her behavior for a very long time. No, I cannot control her, but I could have, with my husband, stood strong and been a ‘united front’ to let her know that I wasn’t a push over and her behavior wasn’t OK, and I would have saved myself a lot of time spent worrying about what was wrong with me, when the problem was all about her.
Talking to your mother-in-law doesn’t have to be a hearted discussion, you could say just what you think- that the email was meant for someone else and if she is concerned then she can talk to you directly about it. At least if she continues talking about you, you can be sure she will get the email address right next time and hopefully not bring any drama to you. It’s tough wanting to bond with a mother-in-law when she’s not exactly opening her arms the same way you might want her to. Good luck.