Women shouldnt be trusting their kids to be alone with anybody that's not the biological relative like that. You have blood relatives molesting kids, so what about somebody that has no relation. Not saying this guy is or isn't, but too many mothers make stupid selfish decisions because they hate their kid's fathers.
Hypothetically if I were in a step dad situation I would check with the biological father on everything. Men need to work together instead of trying to one up each other just for the sake if impressing women.
I wouldn't be doing certain things unless the biological father was dead or something. The kid already has a dad, he doesn't need me unneccessarily doing things his dad does. If you truely care about a kid you're not going to try to make their father look bad(not saying this is the case) because at the end of the day that is still that kid's flesh and blood as well. In this case I think the stepdad/boyfriend whoever was not thinking this through and the woman probably leads the relationship.
The kids biological dad should not have let his anger show like that. He might be right, she might be cheating on the current bf for all we know lol