I’m so sorry. I’ve had similar things happen with therapists and it can feel just devastating. The thing about good boundaries is that you state them, you don’t talk about the reasons for them.

So for example she could say: I can’t always answer my emails very promptly (not that you expected her to) and then if necessary you could discuss how you might deal with that.

The why of it, that she needs to protect her family time or polish her lacrosse trophies or whatever is irrelevant. (I can’t believe she said that she needs to protect HERSELF and her family from you or that she dreads your emails. That’s awful. Even though I agree it was clumsy wording and not meant to hurt you.)

This is about her. She cares a lot about you but hasn’t figured out how not to overpromise emotionally. She’s overpromising bc you truly are in her heart. But she needs to sort that out on her own. That’s her effing job. She cannot be blaming you for her feelings.