At a loss and feeling like a crappy mommy

I don't know how to deal with a 3 year old.
I don't know if Lauren is spoiled, scared, overwhelmed or pigheaded in most situations.
Swimming each week is a total disaster. She screams, cries and throws a tantrum for the entire 30 minutes. Sometimes she says she is scared and maybe she is, but she is also not in control and that's probably her biggest issue.
We went to the Santa Clause parade today and she freaked out. "Too loud mommy!" Maybe it was but does that warrant bursting into tears?
Then we went to Nana and Grandpas for dinner and she refused to eat dinner and cried for over an hour and then when the cupcakes came out and everyone else got to have one she really lost her mind.
She refuses to potty train, cries every morning when I drop her off at daycare, screams for daddy when she's with mommy, cries for mommy when she's with daddy.
I find myself dreading these moments that occur every.day. I feel like she is running the show rather than her parents. We need to figure out how to manage her behavior, how to deal with the tantrums. But how?