You "doubt that situation?" In America if you die your spouse and minor children are entitled to Social Security benefits. If you' are or were in the military, depending on length of service, your discharge and all that they are as well.
Those rules should not extend to developmental decision making. We aren't talking about when they should brush their teeth and go to bed. These are issues that should involve only the mother and father, and Nemo should be cognizant enough to stay out of that process. "Ask your father" is the correct response, in my opinion, if the kids ask her a question about it. She is the man's girlfriend. She is not the guardian of those children. I hope she understands that.
I would be furious if my son's mom allowed her boyfriend to decide what is or is not appropriate for my kid. Just the other day my son called me from her boyfriend's house to ask me if he could watch one of the Harry Potter movies. We make those decisions together. I imagine that you wouldn't take it very well if Juli moved in with another man who made judgment calls about E's recreation without including your input.