I am no expert, I can't see your child and I have only a snapshot but I wouldn't necessarily be worried at all. It all sounds within the normal boundaries of parenting a 3yo. I'd be particularly reassured by the fact that she's not like this at playschool.
I am a leftie liberal, hippy type parent so please feel free to ignore me. My dd is 5yo and also went along to a preschool setting at 3yo. It's an interesting age because they're not toddlers anymore, they crave independence and control over their environment but they are also easily overwhelmed by the world. It's managing the fine line between the two. While we didn't deal with the range of behaviour you're seeing, I did and do have an extremely independent and imaginative little girl. She was desperate to do everything for herself. I know that had I started 'babying' her by putting on her coat and shoes, she would have been similarly disgruntled. What had to happen instead was that we had to be out of the door at a certain time but with her feeling in control of her own self. So from picking her outfit (offer two options if you want a limited choice) to dressing herself, she knew that she was allowed to do that. Alongside this, she knew what had to be done by the time the big hand got to x place, so she was offered the chance to manage her own time, warned well in advance that if she wasn't ready then I would have to help. It was up to me to provide sufficient time for her by being up early enough and prepared. Control over her environment also extended to 'which cereal', 'which music while we dress' etc. She was actively involved in the morning, not told what to do, nagged and harangued. You can also start to employ a legion of dull games such as 'bet mummy can put her coat on first', 'race you to put hats and scarves on, winner gets to unlock the car' etc. It's tiresome but you work together instead of against each other. Give her jobs, involve her in the morning processes instead of nagging her alongside them.
All the normal stuff applies too. Sufficient sleep (she sounds v busy, make sure there's unwinding in an evening and an early enough bedtime), ignore the small stuff, do not let the big stuff go (big stuff is the hitting and being up in your face), try and intervene before a situation escalates (with big distraction, chatter, moving the moment on), praise praise praise the good stuff, talk endlessly to her, chat, play, tell silly stories. Engage her positively. And model what you want to see. I know it's easy to get cross, oh believe me I know, but calm voice, organised morning, have fun, enjoy each other.
The wee accidents are normal. They can regress slightly. Just get her changed, remind her to use the toilet and move on. They seem to have lapses for a couple of years. The waking in the night (if there's nothing worrying her, no pain, no illness etc) is usually linked to development. I think she's probably growing up very quickly. DD became a bit unsettled around the same age and actually what made the difference was mental exhaustion. Preschool taught her to read (she was showing an interest and beginning to read simple cvc words) and the mental exhaustion was what was missing. Doesn't have to be so structured but would she like to do some projects like growing some seeds with you, learning about plants and growing. Perhaps use the local library to get some age appropriate books and do some sneaky teaching. Nature walks, beach if it's close, counting things, playing shops. In fact you can take her shopping for her very own soap, something brightly coloured and in a plunger thing to encourage her to take responsibility for washing her own hands. Perhaps draw a picture together for the bathroom wall to show everybody in the house how to wash their hands after using the loo.
I know I sound like a woolly parent sometimes but I really do think engaging with my dc and showing them how to be a happy, involved member of the family instead of fighting against their natural desire for independence makes for happy, kind and well adjusted children ime.