Being ok with a very unhappy customer

I run my own coaching business and have a small team to support me.
Recently, a customer was unhappy with something that happened in a group class, and we weren’t able to find a solution that pleased her. To bring the matter to a close, we refunded her, even though it was against our policy and not really justified. But since then she’s continued to be angry – she sends the whole team emails criticising and complaining about us, and seems not to be moving on at all.
I’m trying to stay in a place of compassion for her: it’s clear that she’s trapped in a painful model herself and is seeing this whole situation quite differently. But I can’t help feeling terrified: what if she tries to harm my business? What if she succeeds? What if she convinces other people I’m a bad coach and I lose business because of this?
I know I can’t control other people, but the ‘what ifs’ just keep coming. It feels dangerous to have somebody out there saying these things about me, and I don’t know how to feel secure in my business again.