I read your post last night and it made me so sad!
Firstly I think the fact that after school playdates aren't being reciprocated could be for a number of reasons. How does it go when they are at your house? Do they play nicely? Are you on friendly terms with the other mum? It doesn't mean you need to join any cliques, but being approachable is really important I think. There are a couple of mums at my children's school who seem to have an invisible bubble around them saying "don't approach me!" and even I (quite friendly and sociable) find it hard to start a conversation with them because they don't seem to want me to. I did approach one recently and she actually seemed really pleased. It was tricky as there was also a language barrier to deal with but I was surprised by how pleased she was, you would never have guessed.
It shouldn't matter when arranging playmates how friendly you are with the mum, but unfortunately it does. I think particularly when they are small and you would probably go with them and stay for coffee. The other mums aren't going to want to hang out at the house of someone they don't know at all, and so I think it is important to chat and be friendly. My daughter is the same age as yours and we have always had playdates with my friends and their children. It is only the last few months that we have invited one over whose stayed here on their own (without mum) that was a school friend and not a child of one of my friends, IYSWIM? I think as they get older it will be less of an issue.
It doesn't explain why your daughter hasn't been invited to theirs though. Do you have any gut feelings about that? I would invite them again, because when they have been to your house more than one it will be harder for the other parent not to return the invite. Still rude not to though! Perhaps they are just being lazy.
My daughter is quite upfront with other children and asks them to go to their houses. I have brought it up in conversation with the other mum before and said with a smile "oh xxxx keeps going on and on at me about coming to play with xxxx at your house next!" whilst laughing about how forward kids are. Pushy but works!
It could even be something silly such as you having a bigger/nicer house than the others and on seeing yours are too embarrassed to invite you to theirs.
From one persons perspective being friendly with other mums at the school is being in a clique, but to others it's just being friendly. It depends on your perspective.
My cousin has children at the same school as mine and has had similar problems to you and your daughter. Once my children started there I realised why. My cousin is very standoffish and doesn't approach other mums or dads. If they approach her she is chatty enough but they often don't because she has that invisible bubble I was talking about (complete with unintentional "I will punch you if you come near me" face which is only visible when not smiling). This has effected her daughter because her daughter has learnt her social skills and how to deal with situations like this from her mum primarily, and so the daughter doesn't know how to approach people either. For her the problem sorted itself gradually as new children started and she now has a couple of children she likes.
A friend of mine has the same problem with her youngest child and it's become apparent that the child doesn't want to play with others in her year because they are all imbeciles!
Another also has this problem and it appears that her child may have some mild SN. Possibly ASD/AS/PDA. She is being assessed. It means that she appears very advanced in her social skills but actually can't relate to other children. When she is talking to adults she is mimicking what she sees other adults do but can't do the same with children. This is probably not relevant but thought I'd mention it.
The other thing I thought of reading your post last night is that my own child went through this is reception and year one and it turned out to be not quite as it sounded. She said that no one would play with her, but on much further probing I found out that her idea of other children playing with her was if they all did exactly what she said and let her control the game. So when they didn't let her control the game she would wander off and sit by herself and then tell me no one would play with her. After a chat about the difference and explaining that she needed to let other take control sometimes too it sorted itself out.
My daughter is drawn to the slightly crazy kids with good imaginations. I don't agree with the previous poster who mentioned clothes and music etc. I find that the only ones of that age (mines the same age as yours) who are into those things are the ones whose parents encourage them to be into those things, which I don't. It's never been an issue for my daughter as she has no interest whatsoever and neither do any of the children she plays with. Personally I think all that stuff is a bit old for them, too teenagery, although my daughter is probably quite young for her age and still more playful. She also likes playing with boys quite a bit. I wouldn't limit it to just girls if there is a boy she gets on with.
I wouldn't give up on Brownies. If I were you I would go back and tell them exactly what the problem is with her finding it hard to make friends to the point where she is sad and losing confidence. Don't be passive. Tell them and ask them directly to help her. I can't see them not wanting to.
My children's school have a area where those who are quieter can go and read or play puzzles, there is also an area called the friendship zone or something where children who are lonely or want to make new friends can go and older children play with them all and get them playing together. I was going to ask if your school has similar but it sounds as though it does which is great.
Do you have friends who come round with their children or who you meet at the park? Are you sociable yourself?
Also, where do you live? I'd more than happily engineer a meeting between our children (at a park?) and then invite your daughter over (with you of course as I am a weirdo stranger off the interweb). She sounds lovely and my two love new children to play with!
Sorry for the mammoth post!