OP I've worked as a nanny and I am currently someone who employs a nanny.
Calling them 'girl' and talking casually about firing them is disrespectful. Your child was happy with the first one and you fired after two months for the sake of dirty dishes. Your child is happy and attached to the current one and you're being odd with her as well.
The fact that she accepted one rate of pay so recently and is now, so soon, asking for a significant increase suggests to me that the duties in the role are in excess of what she expected. Could that be the case?
Did you spend time explaining your expectations and outlining the role?
For example, I've told our current nanny to prioritise engaging and playing with the children over household chores. If she's on the floor playing with them with a stack of dirty dishes next to the sink- I am happy.
I would be equally within my rights to ask her to clean dishes and fold laundry- but then I couldn't complain if I came in to see the children parked in front of Bluey while she did it.
It's about communicating your expectations and priorities. The same as employing anyone in any role. Do you manage people in your career? A nanny isn't much different. Tell her how you define success in the role from the outset.
If you're particular- then know that about yourself and accept it. Set out a clear list of duties and expectations, don't expect her to mind read. If you want xyz done during naps or whatever, then say so.
You need to have a look at yourself before you employ anyone else or you will keep having the same issue. It's not fair to your DC to have a revolving door of caretakers