Tantrum city

My 3 old girl is crrraaaaaazy! Tell me this is normal please?! I will give an example of two incidents just today…. 1. Trying to buckle her in her car seat at Costco; screaming from the top of her lungs, kicking, everything you name it. Finally got her buckled and we’re driving and she gets sooooo worked up she gasping for air. 2. Bath time. Normally she’s fine to take a bath, tonight and last night actually, it wasn’t happening. So because she didn’t have one last night she needed one tonight. Same thing. Just absolutely distraught about the whole situation. And when she’s in these crazy tantrums, she is like only fond of one parent. Tonight when my husband tried to grab her she flipped out out and basically said “ get away from me I want mommy”. But there has been times when she’s wants nothing to do with me and more him. Anyways… I just have to know if this is normal typical 3 yr old behavior. She’s my oldest, my son is 1, so this is all new to me. And how did you Mamas handle this situation? She’s extremely stubborn and hard headed already, but when she’s pissed. She. Is. Pissed.