What your ex is doing is abuse. You need to make sure that you get all your evidence together, in one place (print out screenshots of texts, emails, etc.
When dealing with a master manipulator, you absolutely must make sure everything is in writing, so emails are the preferred method of contact.
From here on out, keep a journal of everything. Every single time they leave for their dad’s house and what happens when they come back.
With regard to DD and periods. Get a pencil case and fill it with pads (with wings, so she knows it’s secure), some of those nappy bags (you can get biodegradable ones), and a spare pair of undies. Make sure that you show her how to put the pads on, and that she should secure them in the bag. Hopefully this will take some of the anxiety away.
Next step - take them to the GP, explain about the anxiety. Get everything documented. Allow the children to speak to the GP alone if necessary, so that there can be no accusations of leading the children, or scripting conversations.
With regards to your own mental health and absurd accusations - first, go and speak to your own GP, get a referral to a counsellor and get some assessments done for PTSD, anxiety and depression. Getting assessed can only help you! How? Because then you can show that your own mental health has suffered because of him. You didn’t just suddenly wake up one day and you were a “wobbling mess”; he did that to you.
If you don’t already have one, get a solicitor so that they can also document everything and speak on your behalf.
I'm assuming you’re in the UK. Do children have an advocate for family court? If not, can they get one? Someone who can speak for the children and who’s independent would be a good idea.
Finally, I’m not sure if things have changed over there, but at one time, family court proceedings weren’t allowed to be spoken about. If that’s still the case, be careful about what you say.
I really hope that things will change for you and your children and that your ex and his new partner come to realise that you cannot be bullied anymore ❤️