Sounds like the ex is insanely jealous of his relationship with his DD. Perhaps she's worried that he won't love new DD as much as the first?
It's totally unreasonable and very immature of course, but by slamming the door shut on his relationship with DD and you she is probably making it much worse for herself.
I'm not sure how happy I'd be for my DP to have everyday access with a key to his ex's house and spend all his visitation time there if I was his wife. She's made a bit of a rod for her back there by effectively banning them from her life. She must be twisting herself in knots when he is at yours in the evenings.
And as mentioned, she's just going to sit at home alone with the baby when he is at yours? What do her family think of all this? For goodness sake sometimes I wonder who the grown ups are in relationships these days.
And she had no right to deprive your daughter of a family life.
You both must stop facilitating her. You should tell him that you are going to mention it to her, and leave it up to him to decide if he wants to be there.
At that age I don't think the wife part will matter too much, as the possibility of a sister will outshine that topic. And let them deal with the excuses of why she can't meet her. Show them up for the ridiculous pair they are.
I agree with the DNA test. Put that shit to bed and call her out. Because if DD does meet her sister you won't be there to protect her from a potentially venomous woman.
I only hope to god that having a child makes her look at life from a different perspective.
I'd start discussing different visitation patterns too...when the heck do you get a break?