It's normal. ALL kids this age, at some point, go through this. Some even hit and push and bite. It is also the "terrible 2's" age. It's all developmental.
Head's up... "terrible 2's" does not end at 2 years old... this "stage" goes on until 3 and 4 years of age and hopefully by 5 or 6, it goes away. There will also be LOTS of tantrums as well. This is all part of "ages and stages" and is developmental based. They are learning socialization, boundaries, cause & effect, and on and on. They don't automatically "know" how to play. Also, remember, that kids this age do NOT have impulse control yet. FULL impulse control does not emerge until about 3 years old.
Whichever method you use to teach your girl, just make sure is it age appropriate. Their cognitive ability is also developing still. A child will not automatically "stop" a behavior in one time. It is an ongoing developmental phase. Then it will stop, and another phase will emerge before you know it.
Sure, teach her "gentle" and "soft" etc. Distraction and redirection is also beneficial. Sometimes, you just need to redirect the child instead of "lecturing" the child. At this age, wordy lectures will not work, as their attention spans and focus is not lengthy at this age. Sometimes you may need to stop their hand gently when they pinch or pull, and hold their hand in your hand and say "no pinching/hitting/pulling etc." Then put the child in another area momentarily away from the other kids... and she will quickly get distracted with something else. Then when all has passed, you can join the others again. Use your tone of voice too.... gentle and firm... squat down to the child's eye level, look at her, tell her "look at me" and then say "no pinching..." You can't really expect them to say sorry each time.. but kids learn by repetition too. It can take hundreds of times, but they will learn. Patience. She will grow out of it. It's the age. Don't expect a change overnight.
Good luck and take care, your girl is normal and like any kid her age. Remember, keep expectations and "correction" age appropriate too. You will need to pick your battles so to speak.. there will be many in the months to come as they develop more.
~Susan
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