Hi L.,
First of all, you have my heartfelt empathy. I once cared for a little girl who went through exactly what you are describing, and it was so hard for everyone.
Let me say, first off, that this heightened state of emotion at this age is very typical. There is a series of books called "Your ___ Year Old". I can't remember the author, but they've been very helpful to parents in understanding each year and the phases we adults might see manifest.
I learned (with the child I cared for) that I had to very directly attentive at playdates, present at all times. I tried to keep the conversation around what was going on as factual as possible (because she's already emotionally engaged), but the crux of it seems to be about having control of her surroundings. Playmates didn't care for the bossy directions, but if you notice what's at heart is also the desire to win or dominate the situation. This in and of itself isn't necessarily bad, and it gave us a lot to consider.
At some point, many kids feel it is important to be the boss, be bigger, be the winner--at all costs. My suggestion would be to set up parallel play activities as much as possible during playdates. Beading necklaces, coloring/painting, playdough or cooperative games. I'd avoid anything overtly competitive, and steer clear of activities/dress-up anything which gives her a chance to get mad because her directions aren't being followed. (These were trouble spots for us.)
Interestingly, children are very self-correcting in groups and there's the idea of the "social contract", in which every child has to take turns being in charge of the play and getting along with the group. It's not so much that the directions are always outrageous, but also that she has to be willing to comply with the other child's direction. If there's no back-and-forth sharing of directing the play, then problems can arise and the group may try to bring the nonconforming child into line, often with very emotional results. Adults do this with each other too, only hopefully more gently than children who haven't developed a sense of tact.
And yes, sadly, sometimes their 'great big noisy fuss' (to quote Beverly Cleary) has to be taken to their rooms. More than once I've had to remind children that "This is a time for talking, not a time for tears" and invite them to come back when they were ready to listen/problem solve. We don't need to banish them, but when the screaming and tantrums ensue, at this age it's okay for them to have some context around taking a few minutes to work through their feelings and cool off. Some playdates ended with me playing with the other child alone while she screamed and vented in her room. Not pleasant, but it also helps to pull the larger group out of the vortex of emotion that happens and move things along.
Once again, so sorry. It's hard. Also, one more thing: if you haven't introduced your daughter to Ramona Quimby (Beverly Cleary's lively and spirited titular character), this is a great time to do so. The first book in the series showcases Ramona experiencing many of the same feelings, and might be a non-confrontational opportunity for her to reflect. I wouldn't try to teach from it, just read, and see what comes up. And hang tight-- I've never seen a phase last 'forever'--although when it happens for the umpteenth time, it sure feels like it!