You need to first off speak to parents about each issue and find out exactly how they handle this at home. If she doesn't act out at home ask the parents what her response is if they say no. You probably at this point will find out they give her everything she wants. Suggest that if there is no reason to not say yes that they perhaps make her wait for things or do something in exchange for her treats to teach her some patience and tolerance. Explain to them, without any sugar coating the things that are going on and the effect it has on the rest of the group including your family. You can make it clear that you want to work with them to deal with these issues but can only do this if you are on the same page doing the same things at home and at daycare.

At daycare I would put her on time out EVERY SINGLE TIME there is an issue. If she talks while on time out, I would use my stern voice and cut her off and remind her that she is not allowed to talk on time out. Why not come up with an activity to do with her while the toddlers are doing free play and use a big piece of paper and crayons to come up with a list of acceptable behaviours. Obviously she can't read it but it's more the action of doing it. Alternatively have her talk to you while she colours and discuss what behaviours are unacceptable and what her consequences will be. Ask her how she would feel if another child did x,y & z to her. Every morning when she comes make it your first stop with her to go over ground rules by asking her what is appropriate. Have her mirror those rules back to you and ask her what happens if she doesn't stick to the rules. Constant reinforcement and reminders will eventually have an effect. Honestly, I think this kid is probably bored. Kids this age need to be in a group with kids of a similar age generally, not always but quite frequently they thrive better that way. What this child needs at this stage though is discipline and it needs to be reinforced at home and you need to tell the parents this. She needs to be accountable for every bad behaviour and that is how she will learn. Praise her when she is good but every time she breaks a rule that she knows full well she shouldn't..... time out. Yes it will likely be an all day event for a little while but that is how she will learn. Don't be passive about it, don't scold her in the same tone of voice as you praise her and that way she will know you mean business. A passive approach is like talking to a brick wall so honestly put your business shoes on and kick her into touch, no actually kicking though lol If her parents won't work alongside with you, then terminate for the good of your group and for yourself.