Don't let the fit last for 30 minutes again. That's way too long. Stop it immediately or else you're setting the stage that it's ok to throw 30-minute fits.
Do whatever your method is as soon as you see the fit coming on....whether it's time-out, naughty spot/chair, spanking. Be consistent with that method. if time out or naughty spot...one minute per year old is what's recommended by child behavior specialists.
Tell her immediately when she talks back and kicks, "That's not a nice thing to say. You don't talk that way to Mommy and you don't kick Mommy. Those were bad choices. time out..." or whatever you use. She needs to know that bad choices lead to immediate consequence.
When the timeout is over, ask her if she knows why she was put in timeout...tell her to repeat it to you. And if she does that action again, that bad choice, she'll get another time out. Ask her what a "good choice" would be.
Kids like to feel like they have some control over the issue. Showing them that there are choices in life displays that they are in control of their consequences.
Perhaps, when driving to church ...prepare her for what's coming. In a cheerful voice, ask her if she's excited about playing with her new friends today and Ms. ____ (her teacher's name). Ask her what her favorite part is about school. Just to get her excited about the day. And when the crying happens, just ask her directly "why are you crying?" and reassure her that "mommy always comes back to get you, right? I'll be back before you know it. You're going to have so much fun with your friends, playing dolls and dressup." And try to re-direct her attention to the toys in the room or what her friends are already playing with...this helps if there are already kids there, so try to not be the FIRST arriver.
Has she been in kids' Sunday school before - where you have to leave her in the nursery during church services?
My son's been doing this since he was months old and he's been through phases of being clingly, but nothing this harsh. The re-direction and seeing other kids playing always made him immediately forget about mom.
Good luck!! she'll get beyond this really soon, I predict. She just needs to see that this is a regular thing.