I don't do playdates nearly enough. there are a variety of reasons: I'm a single mum running a business fulltime single-handedly and I find it hard enough to manage twin sons aged nearly 9 alone, let alone other children; DS1 and DS2 are incompatibela nd have v incompatible friends who don't at all mix and if the twins each has a friend round, it's nightmare to supervise and really hard work; never get enough time to tidy and clena house and ensure we're always stocked up with foods and would be ashamed to have other people around more often. So I tend to wait till I've had time to clean/ tidy house and buy in foods and have planned activities in advance and different 'territories' for each twin and friend; I love my own company and find the chaos of a group of children really hard to manage for any length of time, plus the parents calling in at start and end of playdates, with all the children milling round and shrieking and fighting.
The most successful playdates are if one DS is at another friend's home and the other twin has his friend here. Then it's almost easy - but this happens v v infrequently.
Finally, trying to coordinate having a friend around for each of the twins at the same time, with no one ill, is v difficult.
I don't know why the other families don't have your DD around OP but maybe it's because if's so wonderful to have your DC invited elsewhere, so you get a break and can get on with things, that they're happy to maintain the status quo? After all, it's like free babysitting.
My DCs were only both invitied to a playdate at same house when they were much younger and even then it didn't always work for the other family, as my twins are so incompatible. But for me, it was absolute bliss to get some time alone to get on with things.
Why don't you, next time you see one of the other mums, say something, in passing like, "DD would love to come round to yours next time as she's dying to see X's toy/ doll/playden etc etc?" Is there a good time we could fix this up? How about next Saturday - or what's the best day/ time for you?
Then you'll get a better idea about whether there's a particular reason why they haven't had her round.
In my childhood, there were 3 of us children and the number of playdates we ever had was so few throughout the years, it was v memorable. I think that might be another reason why I don't easily do playdates. It's unfamiliar territory to me and yet I know it would help my DSS socially. It's just that I came from a family that was largely 'sufficient unto itself'.