Is it Amber and Veronica’s children or Amber’s and Veronica’s children?
It could be either, depending on what is meant.
The first refers to the children Amber and Veronica parent together; the second to two sets of children, separately parented.
So, you would say Amber and Veronica’s children are in regular contact with their biological father but Amber’s and Veronica’s children went on the school outing, travelling in separate cars.
Things are different when you combine a noun and pronoun in the same sentence, however.
This is correct: Angela’s and my view is that …