@IVFdreams2021
The OP has to accept that this woman and the OP's partner are family to this child as are the OP's children and her in-laws. That does not mean that the OP's partner is building a family with his ex , and the OP needs to internalize the difference.
Neither OP nor her partner have any control over what the woman says or does. They can choose to largely ignore it or they can engage. If they choose to engage, they should do so with the full awareness that they have no real ability to effect any change in the ex's behavior.
For the OP, I would imagine the real difficulty will come with the realization that her partner and his extended family will likely come to love and accept this new child in much the same way that they love and accept her children. If they are good and decent people , they will see no difference in the children.
As much as we do not like to think about it, any man who has had sex with a woman could possibly have a yet to be announced child somewhere out there. There is no form of contraception that is 100% effective. It is a statistically unlikely occurrence, but it is certainly a possible occurrence.
Maybe it would be helpful for the OP to get some counseling or therapy in trying to navigate this difficult and unexpected situation.
It can hardly be an easy situation for either the dad or the child , and nor can it be an easy situation for OP's children to grasp.
Seemingly, the ex may not have a very mature or realistic grasp of the complexities involved and her responses seem more like that of an immature teenager rather than an adult in the midst of a serious situation.
Unfortunately, you have to take the parties as you find them. Regrettably, this ex brings little to the table that is likely to be positive .