From where I sit, we are talking about the mother-figure this child has known for most of the child’s life. The woman is remarried with a baby, and OP says the relationship she has with her husband is great and there is no feelings on either side for the other. There are no trust issues and he has decided to keep the ex involved, wisely, and she has accepted.
Now she has a child who’s having a birthday, a child who will be raised closely with the stepchild, and somebody who’s clearly important to this mother figure of the child. She had invited the child she helped raise for more than half the child’s life, the child’s father, and the child’s new wife (OP) to the party.
I’m really not seeing where the problem is here.
I see two adults being mature about the effects of a breakup on a child who lost their only mother figure until OP came in the picture, and while the OP is insecure about it (which is understandable), she is handling her insecurity in the wrong way. If she was really nervous, go to the party, bring the child, meet the family, and see that shared parenting responsibilities across two households is not in and of itself an attack on the new relationship, but a support for the child who had attachments in both households.
My husband’s ex used to invite us and our child to birthday parties for my stepkids, it had nothing to do with secret feelings between the adults, it had to do with loving the kids enough to put the dumb grownup stuff aside for the comfort and security of the kids. We also used to have dinner together, meet at the playgrounds for everybody to play, and stuff like that. For Halloween this year, I invited his ex and her new boyfriend and their shared child, why? Because we had the kids for Halloween and I wanted them and their child to feel like they are a part of the kid’s holiday without needing to choose sides. For their child’s birthday, I’ll send a gift. Why? Because that child is my stepkid’s sibling and an important part of their lives. I want to make sure that the kids see I acknowledge that and I celebrate that bond like they do. Same reason I’ll give the a Christmas gift to their sibling, stepfather, their mother, and their mother’s parents.
You have to decide, when you’re part of a family like this, do you want to be a paranoid warden who goes on the defensive whenever somebody vital to your stepchild comes into their life? Or do you want to accept that a whole life happened before you came along, and that includes a child, and for the health of the child and the marriage you will have to accept that your parenting team is made of two households. If you walk into this and lay down the “her or me” law, you will only do two things... Alienate your husband and make him feel you don’t trust him and hurt the child. He will start keeping from you when he talks to this woman who’s a part of his child’s life. Then your paranoia will really be a mess.
If the invite was for him and the child only and specifically excluded you, that would be one thing, but that’s not the case. I say go, have fun, let the child enjoy time with the child of the ex, and see for yourself that everybody has moved on from this relationship but still has the health of the kids in the forefront. IE, they’re behaving like rational, mature adults.