V.W.
I don't know about normal... but I would DEFinitely limit her playdates to the time that prevents her from having a meltdown. If that means 50 minutes, so be it.. or stop having them altogether for awhile if limiting the time doesn't work for you.
imho, that is the biggest reason for preschool (not academics)... helping the kids learn to adjust to being and behaving in social situations and how to handle not always being the center of the universe. How to wait their turns and how to share and how to have delayed gratification. All things they should have been learning at home all along, to be sure, but also things that they don't usually have to SUSTAIN for long periods of time at home.
Give her a break from it. Then give it a go while limiting the duration of the playdate. Slowly, as she has success, increase the time in small increments. Be sure you discuss this with the other mom beforehand.