Custody Exchange

My SO was just awarded joint physical and legal custody of his kids, but the mother apparently still has a problem and doesn't want me picking the kids up if he can't make it. She keep saying that the court told them to not have anyone else involved. There have never been any physical altercations between the two of us and the last time we even spoke was over a year ago. We haven't read the final order yet to see exactly what it says but I don't recall them saying any such thing in court.  There are times when he works until 9pm and they have to be picked up at 8pm. Their bedtime is 8pm and these boys are ready go to bed on time. We usually change them and put them to bed right away so they really need to be picked up on time. Not to mention if he's late I'm sure she'll be the type of person to take him to court over it and try to get the times amended so that she has more time with them than he does. Do we have to take her to court in order for me to be able to pick them up?  
We've been living together since before the kids were born and are engaged to be married next year. The kids have known me since birth. The only issue with picking me them up is her. Edit:  for some reason she bitches about his mother picking them up.