I get where you are coming from but unfortunately these are some of the common challenges with blended families and it is unfair to force DD2 to stay away from her cousins wedding. She did not create the blended family.
And OPs DH has also made it clear that he wants DD2 to go if she wants to go, and he wants her to maintain the relationship. He has shown strong support for OP and her daughter so forcing DD2 against his wishes will also cause a rift.
You say she can still go to her grandparents, what of her cousins? From what I read she is close to her family members and while I feel for DD1 I disagree with using DD2 as a pawn and making her love for her sister conditional on not going to her cousin's wedding without DD2.
Unfortunately no matter how much OP wants both girls have different fathers and as a result different families and I am so glad OPs DH is very supportive of her daughter, unfortunately they cannot force everyone to treat her the same and they cannot force DD2 to chose between her DD1 and her other family members.
Going to wedding doesn't mean DD2 doesn't love DD1 but as she rightly said she also has her other family members and she has made it clear she wants to continue to have a relationship with them.
OP and her DH have taken their stand and rightfully so, DD2 should not be forced, it will create resentment and result in more issue between the girls.
As someone who grew up in a blended family I would rather know where I stand and recognize my half sister also has her side of the family and know that I have my relationship with my half sister and that she also has her relationship with her side of the family which I'm not a part of.
Unfortunately while it's not nice, that's the reality of being part of a blended family. OP cannot force them to invite her by keeping DD2 away. She needs to work on managing their relationship in such a way that enables them to understand that whilst they are sisters, they also both have different sides of the family which will result in different levels of relationships for both of the girls.
I don't know what DD1s relationship is with her side of the family but it is not DD2s fault if there isn't a relationship there and she shouldn't be made to pay for it by trying to force DH's family to treat both girls the same when they don't consider DD2 to be their family by blood. I'm not saying it's fair or tight but unfortunately she can't force them.
She needs to accept it for what it is now and manage her expectations going forward.