He sounds very, very controlling.
My friends ex dragged her through the courts, cost her thousands, managed to wrangle custody, and in the end, like this fellow with his first daughter, botched it and my friend regained custody of her child.
This guy sounds so similar. I believe that if he was depressed, narcissistic, and the children in his eyes were a reflection and part of him (according to his way of seeing thimgs) he could be capable of 'taking them out' so he wouldn't be deprived of control, and to his way of seeing things they wouldn't have to 'suffer'.
Moms background is not the issue, here. She's been caring for them all along, and probably doing a good job. Dad sounds like his work, when he was working kept him away from home alot. It sounds like when mom got custody, thats when he 'snapped'.