This is pretty normal kid stuff, in my experience. After all, who wouldn't want to have everyone do what they want to do, all the time?
Although I agree that most of us would enjoy a world in which everyone else did what we wanted to do... I don't agree that melting down in tears over this as the OP described is "normal kid stuff". AlthoughI don't mean that a child who has this happening isn't "normal" - I'd phrase it as this isn't "typical" behavior. By the time they are in third grade, most children have learned to interact with give-and-take re not getting overly frustrated when another child wants to do something their way, and also have learned to hold their frustration in check when they are frustrated over a situation like this.
To the OP, re your dd having playdates and invitations to birthday parties - I'd look more closely at - does she seem to have friendships with other children? Are their children she seems to be close to and care about? Birthday party invitations in early elementary are often offered up to a full class or group to avoid children feeling left out (or just to make sure a good-sized group of kids attends the party), and playdate invitations often include a bit of planning/convenience/etc for the parent as much as for the students involved. As students move into upper elementary you'll see that they students themselves start being less compliant about parent-arranged playdates, and that's when kids who have difficulties with things like this might start seeing less playdate and birthday part invitations. I'm not suggesting that will happen with your dd, just thinking that I wouldn't necessarily use playdate and birthday party invitations as a gauge of whether or not an early elementary child is successful at forming and keeping friendships. I'd look instead at what she has to say about recess, and look at what actually happens at the birthday parties and playdates to gauge how she's doing with social interactions and understanding.
Best wishes,
polarbear
