I have first hand experience of the difficulties that can arise when a relationship with a partner breaks down but both of us still have to communicate in order to parent our children. This can be fraught with difficulties and I am not sure I managed this as well as I would have liked.
In my work as a child counsellor and a Parent-child relationship therapist I have found a few resources that others might find helpful and I surely would have if I had known about them (or they had been around) when my children were young.
Learning about the window of tolerance: https://www.youtube.com/watch?v=Wcm-1FBrDvU
When children behave differently with each parent: https://www.theedadvocate.org/kids-behave-one-parent-not/
Looking for support: https://www.parentingapartprogramme.co.uk/
A couple of books that can be shared with children:
The Invisible String by Patrice Karst
Mum and Dad Glue by Kes Gray
A Book that I believe is a must read for all parents, carers, professionals who work with children etc.
The book you wish your parents had read by Philippa Perry