I understand having children does take time, but I've experienced a parent that ends up being available around 4 hours a day while they are the linchpin in a certain part of the process that prevents a job from being completed. They're slow to respond to messages, emails, and calls and sometimes async responses are just not good enough when we have contractors ready to put equipment into the ground.
Just seems like at some point, the role should be part time and not involved in some crucial aspect of the process. My complaint should probably be towards the company though and not the parent.