Well op, what a ride, a simple question of a child being left out from an invite to a wedding along side the nuclear family, for what it's worth I think many agree with you on that point, it was unthoughtful of them, probably not intentional, but yes unthoughtful.
Your little girl at ten probably was upset at not being a flower girl, they don't understand the dynamics of only smaller children doing this. You could have managed this upset better if she had been invited along side of you but unfortunately they are insensitive people, probably not unknind intentionally just a bit ignorant and not thinking of her and you.
This episode has shone a light into the dynamics of your nuclear family and how future decisions may go, especially finanacially.
There is nothing you can do to even this out, his family will always favour their grandchild and even if you divorce this will not change.
Your influence will not extend in the future by inheritances, this family have purposely diverted and altered their wills to bypass you so your grandchild benefits and other siblings do not. It is not your money to decide what is fair in the future, you have been taken out of the eqausion, they would do this to their other children if they also remarried, it's what people with weath do, it is not exceptional, it is the norm.
I do think your anger comes from the fact your husband won't be the direct decendant of all the money but where there is money even first wives are bypassed becuase of the grandparents fear of death of sons/daughters and the 1st wives/husbands remarrying. It's very normal
Whether you fall out with them will make absolutely no difference to them and your child's inheritance, it will come to her eventally in one way or another. You said you went to private school yourself so maybe your parents have wealth, you don't say about the father's family's finances but this is life, you must have thought about these consequences when you met your current husband.
You will just have to ease your first daughter's feelings in the future, it was always a conversation that was going to be had, I think your anger is not just about the invite but the inequalities of your children's futures, you are transferring these feelings about the wedding to the wider issue of inheritance, that unfortunately is no ones fault, it's just life.
I do think some of the posters are thinking inheritance/property pass on, it would be cruel not to just pass on to the son and allow him to share his wealth with the new family, well some wealth can include more than property it can include money that will continue to generate after death, through products, publishing, copyrights etc.