First, he needs to be careful what he says, he needs a solicitor to review what actually happened and then advise him what not to say, what to say and how to say it. There are ways to state the facts without legally condemning oneself. Saying "Yes but... ." probably isn't the way to go since the opposition will jump on the first word and ignore the subsequent explanation. (My lawyer didn't want me to say anything without his preparation so I wouldn't sink myself. He said his first priority was to sit on his clients so they wouldn't blab the wrong way and make their cases worse.)
As they say in the USA, you're allowed to keep silent or choose your words well, you can't be forced to incriminate yourself.
This is a real issue that he can work on: "he made a mistake when
rushing to take her back to her mother". He needs to stop and think. It is better to be a little late than have something happen that could make things even worse than they already are. He needs to look at the big picture and not always be in
reactive mode. Over time he needs to switch to
proactive strategies and actions.
Does he have a solicitor? Does he have a proactive strategy to demonstrate his is a reasonably normal parent and not an ogre as she claims?
In my case, my ex always claimed I was late to exchanges. Yet I nearly always arrived within the 30 minute time window used in my county. Of course, when I was early and arrived before her, she never said I was early. That's the negative blamer personality, in her perception the rules applied only to me, not her.
The mother of his child was badly abused by her mother
This is a common situation. Or at least it happened to me, though my child was a boy. Within a few years after our son was born my ex chased away all my family and friends, then she focused on me. Her mother (uBPD) and abuser stepfather (uNPD) really messed up my ex. She actually claimed I was the worst sort of abuser and even a pervert. Fortunately the hospital, children's agency, court and the other professionals didn't find it credible, but she still tried, over and over, each allegation slightly different than the failed one before.
I don't know what they call it in your country, but he needs a Custody Evaluation by a very experienced and perceptive expert who is not gullible and easily fooled, not just any name on a list. Court and even the agencies will not dig into the parents' motivations, perceptions and behaviors. A good CE should dig deeper, giving the parents psychological evaluations, multiple sessions with each parent, observe how the children relate with each parent, also how each parent behaves with the children.