OP, I am in the exact same boat.
My DSD just turned 15, I've known her since she was born.
Myself and DH have 3 DC together.
About 2 years ago, DSD stopped coming over; before that she would come over every 2 weeks and be bloody miserable when she was here. Going up to her room, ignoring her brothers, ALWAYS getting a headache.
It was tough work when she was here.
Visiting then became very sporadic along with ignoring calls & texts or coming over to see her grandparents but not us.
A year ago she had a conversation with DH and just said she basically didn't like him.
He told her that her comments really hurt. He backed off a bit but would still stay in touch.
We invited her on numerous trips over the years, always says no.
I feel bad for her brothers as they were very close to her but she started blocking DS (now 12) when he was 9 and trying to text her. He was upset by it all & now rarely asks for her.
It was tough as they would always ask when she was coming over, then it was 'why doesnt she want to see us'.
In the past few months, she's slowly back on the scene and has come to visit and gone for dinner. It was all nice & no issues.
I massively empathise with you as our situations sound very similar.
I'd love for us all to have a closer relationship but it doesn't seem to be on the cards for us.
Poor DH has always wanted to be involved but he isn't treated like the 2nd parent. Sometimes I think he's just seen as an ATM.
He wouldn't be involved in any decision making when it comes to DSD.
I don't think it's fair for DSD mam to say to your DH that DSD doesn't want to come over but will be happy to go shopping & on holidays. DH should address that, along the lines of 'I will be happy to take DSD shopping and we'd love to have her on holidays, however I am surprised she would like to go shopping since she doesn't want to see me. Can we meet up to discuss this'
Talking in person much better than hiding behind an email!!
My attitude at the moment is to still be in touch with DSD, I'll text to see how she is, or we will invite her over.
The lines of communication are open and I just hope one day she will see we aren't bad people & we want the best for her.