It sounds like you handled things fine. You kept calm and collected, you answered his question factually and you called him out on his BS. It doesnt sound like there was anything to validate there. It is hard for me not to get angry at a guy who would do this with a 6 month old baby. You are doing a great job keeping your sh#t together.
Let him set up the appointment with the mediator. Let him do all the work. It sure seems like he wants you to do it for him.
Hang in there, you are doing great.
W 34 Me 42 Married 7 years together 8 0 kids 1 beloved dog BD 4/6/2018 I moved out 4/7/2018 I moved back in alone 8/05/2018 I file 3/06/2019 D official 5/7/2019