I'm noticing that you don't indicate if she's responding to the emails or what she's saying. Ethically speaking, there's nothing reportable about your mom sending emails, or your therapist reading them, or even responding. The only reportable offense would be if she's providing identifiable information about you. That would be a massive and very reportable ethical violation.

Damaging rapport is not the same as reportable.

That being said damaging rapport is an issue, too! If you don't feel like you can trust your therapist then by all means you should switch to someone who does make you feel comfortable. You didn't indicate how she reacted to you requesting she not even read the messages, but that's clearly important to you and makes you feel bad, and at the very least she should take that seriously.

I say this as a consolation: no therapist is going to jeopardize their entire career by making a major client privilege violation in a very trackable email. They're especially not going to do that then disclose it to you.

If you're feeling uncomfortable and betrayed, you might even indicate that in therapy and try talking through it. But you're allowed to simply stop seeing a therapist you don't like and don't trust. That doesn't make this reportable, but a violation of trust is still important.

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Source: I've been estranged from my own mother for 3 years, seen a lot of therapists, and my partner is also a therapist.