M.O.
I will simply say that I was in this same boat with my first child. Very energetic little girl, pushing to engage people, etc. She was NOT trying to be mean, but she didn't understand she was MORE energetic, bigger, stronger, faster than most other kids her age or how to interact with the older and bigger kids she was playing with. I never got to sit down. I stayed with her and would "remind" her how to ask for a ball, how to wait her turn, etc. I never expected to be a hands on/helicopter parent, however my daughter's age and energy level dictated that I needed to be with her.
I envied the people who got to sit by and watch their docile 1 1/2 yr olds playing next to them, digging in the dirt or toddling about. That was NEVER my 1st child (luckily for me it was with my 2nd).
We learned simple phrases like "hands to self", "wait your turn", "say excuse me" as cues to remind her. I must've said these 1 million times.
Although I felt I HAD to stay with my daughter to supervise her behavior on playdates, public places, etc. I feel that I also "got control" of my child at a MUCH younger age than people who seem to blow off toddler poor behavior as "just being kids". My daughter has grown up understanding rules, limits, etc. and just a LOOK from me will get her in line if she's acting up (she's now 6). Yes her toddler years exhausted me. But I feel like it was an investment in her future. What some parents are struggling with now at 4, 5 and 6 we covered well earlier.
Just know that she's too young to "discipline" much. Removing her from a situation is the best thing you can do. Let her know that a "timeout" on your lap if she pulls hair is because SHE was "not nice". IF she can "agree" to be nice, she can try playing again. If she continues pulling hair, the playdate, visit to the park, etc. is OVER.
They understand more than we give them credit for. If she begins to see a relationship between "being not nice" and leaving, she will GET IT.
TRY to be patient, repetitive in your words and consistent in your "discipline" and she WILL GET IT. Yes, it's exhausting. But it's well worthwhile to get control now so that things will be easier as she gets older.
And about your getting stressed out...no one expects toddlers to be perfect. Not hurting other kids, yes we expect that. However if you are "on top of her", I think few would fault you for her toddler ways. Teach her to say "I'm sorry" when she's not nice. And try to take it all in stride.
Best wishes - feel free to msg me if you have more questions. I've been there.