*The girl is not related to this - via biology or adoption, it could have been thought that she would go to her father’s on the day, that she would not be interested in going to a wedding of people she barely knows (as per OP’s assertion) and whom she is not related to.
Once OP’s problem with this was outlined an explanation was offered and invitation given.
I don’t think they have spoken about her as if she is a hindrance, only outlined that she would not be included in a photo with grandchildren surrounding a grandmother and the MIL has stated that she would like some 1:1 time with her actual grandchild.
The vastly different approach to her education is because DH is not financially responsible for her and because she doesn’t have the same inheritance as her sister.
She has two parents who are responsible for her, if they are failing in that responsibility then that is on them.*
The wills are totally reasonable given the blended family situation.
The wedding invitation was thoughtless and unkind and the catalyst for this whole thing. Amends have been made but the hurt is done. ( and imho frankly weird )
This has highlighted the gulf in expectation between DH and OP. This is the problem and why OP is distraught.
Just as DH has every right to his expectations so has OP to hers.