Yes, I think your bolded statement has a lot
to do with it. They would be out of his control. Able to, eventually, do what they wished .. with whoever they liked ... whenever they liked ... and grow to be happy again.
There is no way Peter could possibly have realistically thought that the family could not get along without him. This is 2018. He was an educated man. Our social services system is pretty good (comparitively). Our support networks are pretty fine.
I also think an element of these murders is that he did not want the father to see his children. Without him around to blockade that, the women in the family may have allowed that more and more ... especially as the children got older, and perhaps expressed/demanded their own wishes. Katrina's mum may have eased up on her thinking, Katrina may have allowed more and more access.
A bit of the "if I can't have them, nobody can" attitude.
He said the lengthy custody battle between himself and Katrina "wasn't her at all," but was driven by her parents. "Kat's mum said to me once, "