I think meeting an X's new spouse or fiancé or live in person is different from meeting someone the X is just dating.
Bringing a string of people thru the children's lives can be confusing to the children and the courts can sometimes see it as a less stable environment. So, it may be to your W's detriment in a divorce to introduce the children to her AP. And I don't think there's any reason for you to meet the woman whose mistress is your wife. It was tacky of her to even ask you to legitimize her relationship with someone she is helping to cheat. Your W might have filed for D but it doesn't sound like her AP has so, gross on both of them.
This sounds to me like more flailing around from your W to try to upset you. Not sure what the motive is there.
M: 16y 3 adult kids, 2 young kids H filed D May/15, no svc yet Do I not destroy my enemies when I make them my friends? ~ Abe Lincoln WAKE UP. WORK HARD. FORGIVE. REPEAT.