@Av0bo55
It's very interesting that she does play dates with other children at her house, so it isn't an antipathy to having other children over to her house.
I too would also be thinking "hey I've done 3 play dates for your DD at mine why isn't this being reciprocated?" And would want to ask.
My DD would say something before girl tried to invite herself over again tried to invite herself over again "I haven't been to your house and would like to come over cos that's fair, as you've been over lots to mine"  (out of the mouths of babes..!)
I don't think YABU to expect play dates should be fairly even because it does take supervision, entertaining, effort, food and drinks to do play dates for reception aged children.
So other mum is a bit CF she isn't reciprocating at all. Especially when she reciprocated for other pupils and is perfectly happy for her DD to come to your house for play date with DD. You can discount it being about your DD otherwise the other mum wouldn't let her child come over to your house to hang out with her.
I'd invite different children over for a while for play dates and wait
I had this with a friend of my youngest DD and effectively started saying no to more play dates with 'Susie'. & let my DD say back to Susie (when Susie kept asking to come over for yet another play date or just turned up (!!) - that it was her turn as (DD) she would love to play at her house 'as that's fair' "
You can invent all sorts of convoluted reasons why another parent doesn't reciprocate but really I can't be doing with being someone else's childcare option as I work and am busy as it is. If no return invite after few play dates then there are plenty of other girls for DD to be friends with and in Year R it all turns on a penny anyway, they are friends with who they see most including outside school if play dates are on offer and who they happened to sit next to during that day. Don't store up precedent for a one way play date situ.