I wonder if there is a role for a Guardian Ad Litem for the remaining two children.
I just don't get the feeling that the family dynamics are dedicated to the safety home environment for the children and the parental dynamics are off in this situation.
As long as the father lives at home, he is around those children. What happens if they get a babysitter? Does he continue his Playstation life with resentment to all for what happened? I assume they can pay for childcare, although it is surely difficult to find and expensive. In September, I assume the 5 year old will be attending kindergarten and the 9 year old will be in the 4th grade. That only accounts for a part of the day / night and the mother's job as an anesthesiologist usually comes with dedicated in-hospital call for long shifts that do not fit a 9-5 lifestyle. Do her partner anesthesiologists have to have their schedules disrupted and take more call so she can have more time to supervise the childcare. When she is gone at 2am at the hospital, isn't Dad back doing childcare again?
Optimally, there would be some other family member like a gramma or grandpa or such to be the designated caregiver.
This is complicated and allowing Dad to stay in the home is only going to make it worse.