Ophelia,
Really feel for you, its a very difficult time.
You need to start playing hardball, do not let him dictate the custody arrangements, you need to work out what is acceptable/managable for you at this time.
Discuss with your family, write out a timetable for him when it is acceptable for him to visit the DC,
This way you can get a little control back and also, I would make sure someone is present with you, either in your home or you parents doing this. Do not engage with him
Do not let me take the DC away for an overnight at this stage , it is far too early for both you and the DC. By you allowing him custody on your terms he can't use this against you, as you are not stopping him seeing them.
When he kicks up about this (which he will). Tell him he can't be trusted to take the kids at this point. You need to protect your children and yourself at this time. There is no way you are going to risk your DC coming into contact with that OW.
She has the morals of an alley cat, she is at this time not fit to be a mother, he and other men may think she is great for her antics in the office, and believe he will tell them about it, men can't help bragging, but anyone women who has unprotected sex, gets down on her knees and preforms bjs in the stationery office will really be looked down on by other women and she will knows this. Threaten to tell his parents, friends, everyone if he doesn't play ball. He's the embaressment.
By your telling the girl in the office, you have taken a little bit of control back. You DH may not mind other people knowing, ( his head has been completely turned and she is definately calling all the shots at this stage), even thought they didn't get enough time to put up their act re. the separation and the start of their romance, but the OW will be fucking raging, no woman wants to be known as a marriage breaker. Do you think everyone will think she's so great now.
I can already see trouble in paradise with the the OWs ex coming over and they're all so friendly, staying for dinner etc. I am telling this you, no matter how much he is into her ant this stage, he will get pissed off playing happy families when his kids are not allowed do be anywhere near them. Jesus, she is some piece of work, your husband is such an idiot, he thinks she has it all worked out,you'll be friends with them and it'll all be forgiven, they are on another planet.
I really hope all work out well for you, stay calm, keep a cool head, stay strong, look after yourself and your DC and tell him to fuck back to the Brady bunch if he wants to play happy Families!