OP, a couple of posters mentioned a previous post of yours about the 2 girls not getting on so I had a look.
Since Christmas last year you've made 4 posts, all on the same theme of why you / your DD weren't invited to DH's family events and there are details in these previous posts which are relevant to what's going on between you all and why you initially came up with this idea of how to manage the latest exclusion from an invitation to the panto/Greek restaurant.
Your daughter has a mum and a dad already. She already has her own bio family. The lack of contact with her bio dad/paternal grandparents is for the pair of you to remedy for the sake of your daughter. It is insanity to think that just by dint of you and your DH marrying, you have the right to co-opt his bio family into treating you and yours like their own and including you in invitations. They don't. Their loyalty, first and foremost, is to their actual relative, your husband's daughter who deeply resents her step sister. If your marriage fails, neither you nor your daughter will see them ever again. Same for if your DH happened to pass away.
Have you tried putting yourself in his daughter's shoes at all? She was born of a liaison between your DH and a woman so not into a family situation where the parents are very much together. Fortunately, her dad very much wants her in his life and up until he moved in with you and his step daughter, it sounds like she stayed overnight with him a lot. Now its down to one night a month and the other 29 days she knows her much loved dad is playing happy families in a proper family home with another little girl and a woman who is not her mother. That is a deep source of pain for his daughter. Why would she want to rub her own nose in it by staying the night in YOUR house with you all. It's too much for her to handle emotionally.
While I accept the relationship with her dad isn’t the same as if they lived under the same roof I would argue that they are incredibly close given the unusual circumstances.
In your thread about the lack of wedding invitation for your daughter to the cousin's wedding at which DH's bio daughter would be bridesmaid, you even leveraged the fact your daughter sees him more than his own!!
Money and space isn’t an issue. DH is good to my daughter but doesn’t see why his cousin would see her as a niece but he sees my child more than the one who is a bridesmaid.
She has DH's large extended family which doubtless provides her with love, comfort and support as and when she sees them which sounds like it's not all that often (the panto in question) but you and your daughter want in on that too, despite knowing the pair of girls don't get on. The family know that and will not want to add in more upset for her than has already been the case, hence them not wanting to always include you/DH's DSD. You've said the girls don't have to interact with each other at these events which is laughable.
You really need to back off and to accept that the damage between you and DH's family has been done. You've been married 5? years now and it is evident from your posts that, quite aside from the above, you will have come across to the family as pushy and for that alone you have probably and irretrievably alienated them to the point where you are both tolerated under sufferance. They are very polite to you of course but they will be as you are their relative's wife. Whilst I'm sure they are an attractive family to be a part of you don't get to opt in because you like what they appear to offer. (I'm sure if they were a bunch of low life reprobates you'd be giving your DH every excuse under the sun not to see them, family or not). You really need to reframe their relevance to your daughter so that she understands that she has her own family, your DH's family are not her family, but more like friends, and there may be invitations from them that do or do not include her/you which is all quite normal. You need to work on this now because once the teenage hormones kick in for both girls, this situation is going to become intractable and I would not be surprised if with that pressure and your constant FOMO your DH gets monumentally pissed off and calls time on the relationship.
Maybe post a thread about how to go about building a relationship with your daughter's paternal side of the family instead of your misplaced fussing about not being invited to pantos or private school carol services or birthday parties or the lunches held by cousins you've never met returned from years abroad.
I totally agree that my daughter’s lack of relationship with her actual father has the potential to be more heartbreaking for her than her lack of relationship with her step-sister.
Step families are with very few exceptions an absolute minefield for everyone, but it's the children who are almost completely without agency in their creation, who suffer the most from the casually cruel way adults drag their offspring into their new set ups and abjectly fail to understand the impact it's had on them. Why do you think many parents opt to remain single or at least do not join households until their kids are moving on to their own independent lives? Marry if you wish but no one else has to like it.