As Peg said, the book "how to talk so kids will listen, and listen do kids will talk" is REAL great. AND it is helpful for even adults talking to each other.
I have the book and it is great and gave me insight about adult level talking too.
In addition to everything else... young toddlers go through a stage where they do say "I don't like (a certain parent)." One thing is, don't take it personally... sure, teach her about feelings/communication/what is nice or not... but also keep your expectations about it age-appropriate. Meaning, don't expect change over-night, nor swiftly, nor for it to be perfect. MAIN thing is that that child TRIES their best. Praise her for trying. Not about being "perfect" or not about it. NO child, can be perfect as to how their parent wants. Because... learning will take all of child-hood to get "our" expectations correct, that we have upon them.
Also, the emotional development, of a 2 year old.. is NOT fully developed yet nor its abstract connotations & nuances and understanding yet.
Either, work with her and expect age appropriate things and problem solving on your part, as parents... or, expect her to be/act older than she is in cognitive understanding and impulse control & maturity, and have frustration... for you and her, and battles.
At the same time.. it is REAL important for a child to LEARN about expressing themselves, and how, and how to cope, and how to problem solve. So, sometimes, instead of slapping punishments on the child across the board for anything... teach her how to "problem-solve." If she talks back... teach her "how can you say that differently?" "Can you say it with a smile instead?" Wow, that's better!" and praise her. Thus giving her the ideas and skills to think of OPTIONS of how to behave... and as she gets older, by repetition of this "practice" with her, she will understand better, and it will become a routine... so that it gets instinctual. She is so young to get it all perfectly yet. So there is a learning curve... each child being different. Accept that.
Even some adults don't even have social skills or understanding nor can they talk nicely.
With my kids, that is what I do. Now, when the are icky... I tell them "Redo that... " and they will. To the best of their ability. I accept their effort... and say thank you. I do NOT expect "perfection." Just the effort of trying their best. I give them CHOICES and the chance to REDO their actions/voice/attitude. BEFORE I just plunk down a punishment generically. And I teach them HOW to say/do/think of alternative ways of acting out, but positively or saying it.
Teach her about feelings too and the words for it. happy,sad,mad,frustrated etc. I tell my kids, its okay to be mad/sad/grumpy... but to tell me and we are a TEAM about it and WE will help each other. I am not perfect myself and get crabby... so, I don't expect my kids to perfectly navigate their emotions either. And, when I am crabby, at them, I apologize to them too. It is a 2-way street. They need an example... from us. Not just it being about who is the better Disciplinarian or not. But teaching them over time... about emotional intelligence and competence and coping/problem solving. Little Toddlers can get it... if you start young.
All the best,
Susan