Is it normal for my baby to behave better with others than with me?

Yes: Yes, my kids to it to me all the time! kids know who and will not tolerate bad behavior and usually will not test strangers' tolerance until they get to know them. Therefore, teachers and company get to see their best side while we get the temper tantrums! make sure you are consistent with what behaviors you will not allow and forewarn your children before they get out of the car.

Yes: As you investigate babies every fussy period, feed anytime & carry baby everywhere, you give them an expectation that you are there to do what they want.Strangers don't do that.As they grow older & start talking we assume they will be appreciative & respect our limit setting (better than strangers) but i find that ironic.Kids push back on those whose response they can predict, that means parents.