Let's state this in a different way.
What evidence DO we have?
The husband has clearly behaved in a way which shows utter contempt for his wife. He in no way respects her.
He IS indulging in emotional abuse - the coming out in the way he did, constitutes that. She is distressed.
He IS indulging in an attempt to coercively control her - the verbal abuse he is giving her when she questions anything and his insistence on correct pronouns by her and his children with anything else being 'punished' by his anger and more verbal abuse for saying things he doesn't like.
He IS behaving in a way likely to be causing extreme distress and psychological harm to his children who are at a crucial period in their life with identity formation and learning to understand boundaries. He is using them as a tool for his own identity validation without thought to how it affects their wellbeing.
The question has to become, how does this progress? And what harms are already being done? Will it stay the same or is there a danger it will escalate.
The lack of underlying respect is the problem in this regard. And any woman in this position should prepare for the worst to protect herself and her children from further harm. Note the key word in that previous sentence. He is demonstrating he doesn't have any regards for their wellbeing.
The question then becomes what evidence is there that the wife and children are safe from him if he is demonstrating a lack of regards to their wellbeing?
Yes, maybe you can hope that this doesn't pan out for the worst in a prepare for the worst hope for the best scenario. But the current balance of evidence doesn't bode well for the SIL.
The crucial point is he IS potentially domestically abusing her ALREADY. Legal definitions of domestic abuse do not include the need for physical violence to be present. Whether the SIL (and the OP) are ready to fully recognise this is another matter, but his behaviour in demanding the 'correct' response from her and his children and disallowed them their own emotional responses and questions in order to validate his own feelings is an attempt to coercively control.
Some of his actions already may be starting to add up to a case where he is behaving in an unlawful manner due to his coerciveness.
https://www.cps.gov.uk/legal-guidance/controlling-or-coercive-behaviour-intimate-or-family-relationship#:~:text=Section%2076%20SCA%202015%20provides,and%20B%20are%20personally%20connected
This link has a list of actions that someone coercively controlling someone else may indulge in. Some of the things he has already done, are on that list.
This is why suggestions that the OP should stay well out of it, get to me. If her brother was punching her SIL, the responses on this thread would be different. Emotional abuse isn't properly recognised.
I do think that as time passes, the pattern of coercive control handed out to trans widows and their children will eventually become recognised. But I fear we are some way from that.
In the meantime it's worth reading the experiences of transwidows, the striking similarities in stories and the descriptions in how it impacted on them and their children AND to make sure anyone you know in a similar situation is fully versed and aware of what constitutes coercive control and they are encouraged to take steps inline with that where appropriate.