Yers... it is my job...
Alpha/pack stuff is utter bollocks, because dogs don't form packs nor seek to become 'alpha'.
I suspect (and knowing the breed would help) that your possibly adolescent bitch, got a bit over aroused and over the top and is still too young and immature to know how to calm herself, how to back off etc.
When the dogs were playing, did you observe them (any of them) pausing to check everyone is still into the game, taking turns in chasing/being chased, polite body language such as head turns away from the other dogs gaze etc?
Often what we see as play actually isn't, its more 'testing boundaries' and seeing where they stand with the other dog, and in young dogs that are maturing thats normal. It's about learning manners and where boundaries lie, what's ok and what definitely isn't...
Unfortunately not all adult dogs are good at teaching this to young ones, and young ones are unlikely to teach each other much of use at all as they don't yet possess these skills.
Also unfortunatley the sorts of people who tend to arrange breed meets/pack walks, tend to have no idea of dog behaviour and are die hard fans of the pack theory rubbish and so really don't help matters.
I would spend a lot of time walking her just you and her and rewarding her heavily for seeing other dogs and staying with you, so the sight of other dogs is associated with treats, play, being with you.
I would find some sensible friends with dogs of all ages/sizes/breeds that you can WALK with... but not off lead play type walks, I mean walk together but both engaging your own dogs, walk one ahead of the other, switch around, walk parallel, do bits of training on the way... so that your dog experiences being around other dogs in a structured, reinforcing way thats fun but NOT giddy silly play..
And then I would arrange some sessions where there is a mixture of the above and some off lead time with very sensible steady adult dogs who have extremely good dog to dog skills (this is where you may need a trainer but avoid anyone who tells you their dog will 'put yours in its place' or any pack rubbish!) so she can learn polite manners.
Play should be mutual, balanced, consenting.. it should involve each party pausing frequently to check that the other is still 'in the game', pausing to catch breath, pausing to switch roles.
Play that involves one dog chasing the other with no check ins, no pauses, one dog hammering another, one dog always being chased.. that isn't play, and is likely to teach one dog to excell at being a bully and the other to fear other dogs!