If kindergarten has been in session for maybe 5-6 weeks, how many different methods have you tried in that period of time? Probably WAY too many! Of course nothing works - she's confused about what her consequences are. I'm not sure what you mean by trying so hard "not to give up." Parents don't get to give up. They have to be the grown-up here and set the rules.
She's had a huge adjustment of going to school and being in (probably) a large class with a lot of really big kids in the halls. That's overwhelming sometimes. Is she acting up at school and screaming/saying no? Or only with you? If only with you, then you need to figure out what the teacher is doing that you aren't. Really. Is the teacher yelling at her, "Pick up your things?" No? Then you shouldn't be either. Not sure if you are - you don't say. My point is, if she's behaving one place and not the other, then you have to look at why. If the school has contacted you about her, then you set up a conference and get specifics, find out what the teacher does that works and what doesn't, and agree to some consistency. If she's only doing it at home, then you have to allow her some down time or "re-entry" time with no chores and no expectations other than politeness - maybe quiet time in her room with a book, maybe running around outside for 20 minutes (play catch with her, draw a hopscotch grid on the driveway with chalk, anything).
Now, about the accidents. Again, only at home or at school as well? It's common in school, as kids are distracted by all the activities, don't know where the bathrooms are, don't realize that everyone can't go at once and they have to take turns, and so on. If it's only at home, and you've ruled out medical causes with the pediatrician and especially if this is new behavior, then she can wear pull-ups as needed. If it's pure defiance, then you have to address ALL of the defiance as one problem, not just the toileting accidents.
Tantrums - you ignore. You don't hear them. You don't respond. You have a standard phrase that both you and her father and any other caregiver use. Maybe it's "I can't understand you when you scream. Let me know when you want to talk normally." Maybe it's, "You can scream in your room, and you can come out when you're done." "We don't hit and kick in this house. Go to your room until you can control yourself." What you say is less important that only saying it once or twice (the 1-2-3 method) and exactly the same way. Don't argue with her, don't answer her demands, nothing.
Doesn't pick up her things? Did she do so before and you know that she knows how? I know it sounds silly, but my friend (a kindergarten teacher) puts a strip of tape on the floor and tells them to stand on the tape because 5 year olds don't know what "line up, please" means. So "clean up please" can be confusing too. But I agree with Tadpole about the plastic bag for stuff that isn't important enough to her to pick up. She doesn't want it? It's Mom's toy now. Don't discuss the "terms" of redeeming items when she's yelling. Just put it away for now.
Once a tantrum (or other undesirable behavior) doesn't work for a while, the child stops it. The essential thing is not to give in to the yelling. Reassess your priorities. If she's late to school, she's late. If she skips a snack, she skips it. If she doesn't get to play or go outside because Mom is washing urine-soaked laundry, so be it. The message is, "This is the consequence of YOUR DECISION, dear, to throw/yell/hit." It is not a random punishment thrown at her by Mom, it's HER CHOICE. That gives her the power to stop it.
I think you're probably bouncing from Technique A to Technique B (and C and D) too fast, and no one can keep track. Calm it all down, defuse the situation, and understand that you are in control. Maybe not in that exact moment when she won't do what you want, but within 5 or 10 minutes, she's going to want something that she now can't have because you had to a) clean up, b) wash underwear, c) put ice on the bruise where she kicked you, or whatever. You now no longer have time for her. That usually gets them in line.