I'm sorry you're going through this.
Fellow survivor and SEN mum here. (We also have a pet snake!)
I work in a SEN school, we have Pets As Therapy (PAT) dogs on site weekly. Pets are great for children (and adults), they teach responsibility and empathy and provide companionship.
I agree with above, but understand why you may not want to tell your solicitor to stop the communication. He is attempting to use your solicitor as a mediator, but you have been to court and there is nothing to mediate here. It should not reflect badly on you to ask your solicitor to cease forwarding his messages.
He really is just trying to weed his way back into your head/life.
Unfortunately, that doesn't always stop, not even when they get a new partner or have more children.
The Family Wizard platform suggested above is a good shout. You could also create a dedicated email address that you use for any communications with him... everything can then be in one place and easy enough to find. Then block him and anyone else who may snoop on his behalf from everything else: SM, calls, messages, WhatsApp, other email addresses. Everything.
By taking things like that into your own control, you can build up resilience against him. Messages like the one you received, can be responded to if and when you want to respond.
As a rule, try to give as little away as possible. Don't give him any more information than is necessary. Try to keep your emotions out of communications. Keep to the point and copy and paste your responses when you have already said enough. Be aware of your own responses to, don't bite, take your time and calm down before you respond to messages that upset you.
Over some time, he will see that he's not getting his desired responses from you and he will hopefully perceive his diminishing control over your life, head and emotions.
Well done for coming as far as you have. It's not easy and the court process can be incredibly hard and daunting and I know that nothing is given, even if it should be. If it does go to court, or you are still in the midst of court proceedings, have all of the benefits prepared for your argument to keep your dog and gather any evidence you have of him threatening violence against animals.
Be sure to draw clear attention to this being an example of the coercive control you are still subject to from him.
Honestly though, if he can't afford his own solicitor, he's unlikely to spend the money bringing this to court as a separate hearing.
Tl,Dr: pets are good, especially for kids with SEN.
Prepare for him to bring it to court, tell them it's coercive control, have the benefits prepared on argument to keep your dog.
Good luck.