Monday - I must admit that I looked at this thread, and then went away, but you have since been on my mind so have decided to post despite being a granny rather than a modern mum.
Being a lone parent is hard, even when it is by choice from the outset and you love the role. And you are doing a good job. For that alone - have some 
When it comes to handling a tantrumming, kicking and hitting 3 year old, there are just a few rules that you need to stick to, and then apply them whenever the behaviours happen. Whenever. Wherever. Whoever else may be present. Even if you can see some reason why she has kicked off. The reason is irrelevant, because the response is still wrong.
What she needs to know is that you have an absolute line that she is never ever allowed to cross. And that crossing the line always always results in consequences she doesn't like. And the consequence is always the same. Do not keep varying what you do because the first time doesn't change the behaviour. Its a training process.
You sound very reasonable and sensible, and know which consequences will feel acceptable for you to use.
The response needs to be immediate. And you need to win immediately, because you have to demonstrate who is in control. There is nothing more frightening for a child than to know that no-one is in control, when they have 'lost it'. The time for reasoning comes later. When they are calm. in the situation you describe, I think naughty steps don't work because you are in a battle to keep them in place so the 'fight' is continuing.
For what its worth, this is how I handled it .....
Ideally, the situation would not descend into her hitting, because it stopped in its tracks with immediate time out in her room when she began to tantrum.
I gave one warning as the behaviour started? if you are want to be naughty you will go to your room ....mummy will count to 3"
This gives choice. And tells her what the consequence will be.
If you count, and the behaviour hasn't stopped .....Sweep her up, put her in her room, and do not go back in for three minutes. If she is fighting to come out, just hold the door handle.
After three minutes, ho in.
If all is quiet, give a cuddle, and have a chat about why she felt upset.
If the tantrum is continuing, repeat the choice she has ...count to three again, and leave again.
This might take multiple repeats the first couple of times you use it....but then it really does start to work.
If it had reached a hitting stage before you could stop it, I would have said very very sternly "you never hit mummy! that is very naughty and you are going to your bedroom". So there is no option for her to stop the tantrum to avoid the consequence....because she has already crossed the line.
Then handle as above.
Choice. Consequence........and above all, consistency.
This post was my opinion, and what worked for me before anyone had heard of "naughty steps". If its relevant for you the great. If not, I still think you will do a great job. She sounds a wonderful, bright, little girl, and I am absolutely sure you will handle this stage as well as you have done with the rest of the mothering.