I'll try and explain why the email could make things worse using my experience.
Currently there is the assumption that because 1 gossipy mum has latched on then other parents have also.
Many may not even know who the OP is.
C escalated because K D and M questioned the FB messages. She needed to quickly escalate to drag them back to her side.
How does this happen? It's purely giving 'word' to things.
Any word spoken or typed is open to the interpretation of the reader. What you intend and what they perceive can often be different - even only very slightly.
By typing a message you are giving words to the situation. Words people can interpret how they like. But most importantly words that give C more ammunition. She is then able to take you word and twist it to her own agenda.
In my situation I'm not 1 to post on SM. I'll tell people what I'm up to if they ask or what I've been up to if I ask.
My C was using my sons medical issues as a weapon (encouraging me to talk about them in detail and then picking apart what I said shoving her own examples of how I'm exaggerating in). I gave her that ammunition.
I also took her 4 times after work (I worked FT and she was SAHM) to sort out a family pet. Mutual friends knew this. But only because she told them, posted publicly on FB with gushing thank you texts tagging me or because when asked I said I'd been to see pet with C and how cute it was (C can't drive).
One day a mutual friend asked me if I was free and I said C and I had plans to meet and I was waiting for her to give a time she'd be ready. If she wanted to join I'd let her know plans when I did.
My C then text this friend saying all sorts of things about me. Friend was 
after our communication but didn't disbelieve it totally. Began questioning and then going back to C (unknown to me) and c twisted it all to me being the bad guy. She even dragged in loads of mutual acquaintances and made out I'd done and said things I hadn't.
4 days later C posted something on FB along the lines of kids having forgotten who I am already as I can't be bothered and no one has a right to waltz in and out of her kids lives and the only contact she's had the past 3 weeks is because I wanted to see the pet. (I seriously didn't!)
People began texting me (even they knew who she was getting at). All I replied to things like
"Was that fab post about you?" Is "seems to be"
"What are you going to do/say" Is "nothing"
"Why aren't you commenting" is "because it's a public forum and I'm not into that. Plus I know truth and that won't change".
I never even engaged in those asking. I left everyone wondering what I was up to and how I was feeling about the situation. Initially C then panicked. I assume it's panic. She didn't know what was happening and she'd lost control. She had no more ammunition from me via my own word or anyone else's.
Eventually people started to see C for what she was. Fell over themselves to friend me because they knew I could be trusted. But I kept them all at arms lengths with short non commits and non emotional responses. I'd meet for coffee if I felt like it but again refused to get embroiled in any conversations around C.
Of course I wonder what was said to others who I lost contact with and of course I wish I could set the record straight.
I also wish after the vile things she said about me inventing ds difficulties she somehow now found out he has a very rare neurological genetic disorder.
But what's the point?
I now have a much wider circle of friends, I'm involved in a committee with endless amounts of volunteers wanting to help me (because I treat people well!).
And I know through the grape vine that C is on her 8th group of cronies in the 5 years since this happens and is more and more isolated and lonely.
Serves her right 