Thanks GamerNic for your thoughts. You are correct there was an agreed temporary change in who claimed the smaller amount of Child Benefit for second child, based on written statement from a registered charity advisor (who has since moved to an org supporting bankers) that this would not affect Child TC, double-checked with HMRC by phone. It's young kids; I don't know what ftnae means.
Accept HMRC later writing just to clarify. But just as customers have a duty to respond in a timely way, I believe the office with a non-working telephone number is also violating the HMRC customer charter causing confusion, especially with some language issues and cultural issues (origin as discriminated-against ethnic minority in oppressive state, albeit now a British citizen through residence and work). And there's tribunal decision, the details don't matter as they're not the same at all but this one from 2015 seems to be saying ('here we go again'!) HMRC can't just end an ongoing claim based on an assumption with lack of evidence? [eh I can't include links but hopefully you'll find it or a summary of it if you search for tribunal "2015 UKUT 490 AAC"]
Yes I am sure there is sufficient evidence and supporting statements to show main responsibility, so worth a try for MR and Official Error. Anyway one of the two parents must be the main responsible yet somehow they've managed to award neither parent; if they can remove an award without a reply surely they could have transferred it to the other parent (who is on their system) rather than cancelling.