He is having regular contact from what you say so you'd have nothing to fear from him threatening court, and mediation is a voluntary process, so nothing there for him either.
It's only if he begins a court action that mediation becomes (mostly) mandatory. If he was violent in the relationship, and it was noted in some way, e.g. police called, you can get out of mediation.
As for your real question regarding emails, this is the difficult bit, but you make a rule of
- only reply to anything that is specifically about the contact arrangements. Very short, one-line replies confirming arrangements, or acceding to requests.
- Never reply to deny/defend his accusations. Ignore them because you don't care what he says/thinks, because quite frankly he's your ExDickHead.
This may, in the short-term, escalate bad behaviour because they want, and enjoy provoking you. At this point, you write a very clear 'cease and desist' email.
Dear ExDickHead,
Thank you for confiming you will pick up the children at 8am on Saturday.
Yours, wife you lost.
Dear ExDickHead.
Much of your correspondence to me is unnecessary, and I consider its only intention is to cause me distress. In future, any emails that I receive that I consider as causing unnecessary distress will be promptly, and without reply to you, deleted immediately.
This outcome of this for both us and the children, is that it makes contact arrangements more difficult not less.
Yours, wife you lost.
[If he then gets repeatedly worse, which is likely]
Dear ExDickHead,
As of my email dated X date, I informed you that I found much of your correspondence to me unnecessary and to intend distress.
Since you received that email from me, I consider that your behaviour has worsened.
I am therefore informing you that should you decide to continue in this vain, I will seek independent advice and action to curtail this behaviour.
Again, this will only further sour our relationship, and this will undoubtedly be to the detriment of our children.
Yours, wife you lost.
And then, bloody well go and see the CAB/solicitor/police about a Non-Molestation order.
If it's not that 'nasty' that it requires outside agencies, then yes, just block him, get a different phone no just for him to send you abusive texts with and let him live with YOUR decision.
Your children have to foster a positive relationship, and you cannot stop that. You don't have to put up with him being an arse.