Professor.
Its highly likely that the children's happiness and safety depends on mum giving a damn good fight.
Op, if you can talk to rights of women
www.rightsofwomen.org.uk/adviceline.php
They are very hard to get hold of but they are very very good.
Be calm and no matter what he says or does do not under any circumstances come across in court as being stroppy or bitter. Focus on safe contact rather than contact.
As the poster upthread said use the sturge and Glason report the lower courts have to follow it.
If you have a fact finding hearing ( you will if no cautions or other convictions exist and he Denys abuse) be 100% honest don't be tempted to ham it up or minimise it, all it takes is one bit of dishonesty and your screwed. Be prepared for him to make out your making it all up it remain clear consistent and honest and he will trip himself up.
Do you have good legal support? Unless you are really very savey and very articulate (but that can go against you if they play the "its not fair I'm so stupid and she's so clever she's put me at a disadvantage card) it is essential.
In the mean time focus on how to minimise disruption to the children and maximise safety because if your ex does not seriously fuck up or give up he will at some stage get unsupervised access unless you are really very lucky.
Ways to do this
Talk to your local children's services or sure start centre and directly ask if they can provide you with details of org's in your area providing specialist children's support to children who have witnessed DV (stress that there is no contact now) and find out how you can get a referral.
Don't fret its play based support the kids enjoy it and it does not drag up old memories but they are very very good at dealing with child concerns about contact ( even if you don't know they have them) and will if needed provide prevention support if anything is disclosed that happens during contact.
If your anywhere near me I'm happy to forward you details of the ones we use.
Make sure your children understand about good secrets and bad secrets and that you will never blame them or tell them off for disclosing worries.big up violence being wrong and not there fault.
And most importantly document everything you can of a concerning nature date time what was said who was about that sort of thing and keep every communication from him ( if you can engineer it so its all email or text).