"Where am I going wrong?!?!?!?! I had started to think that things were on the up, but lately it seems as though my daughter's behaviour has taken a nosedive. I think she's just asserting herself but I find it hard to stay calm when she does. She ignores me very often or when she does respond to something, it's usually with a "no" or "I don't want to!". She is 3 next month so it could just be the age she's at."
I can tell by your question that you are really tired and frustrated. I have gathered from your comments that your daughter is throwing tantrums. Tantrums are power struggles. If you give in to them, sign deeply, become emotional, get angry, or turn into a monster then you are showing her that her power struggle is working. This will encourage her to keep going or do more tantrums. She is trying to control your emotions and it is working it sounds like. Don't show emotions when your daughter is raging or she will keep going.
She is trying to tell you something. What is it? You know what she is saying. You may not like what she is saying but you know what it is. Is she saying, "Mom, I want your attention more?" Could she be saying, "Mom show me where my limits are so I can choose to be happy?" Maybe it's, "Mom, I need more structure." or "Mom, help me stay calm; I don't know how." Could she be saying, "Mom, I have anxiety. I want to do certain things but don't know how." or "I want to tell you how I feel, but don't know how to help you understand?" Really take a deep look at her behaviors and what your behaviors are too. What does your heart tell you she needs? More attention, more restrictions, more structure, more acceptance.
While we are on this vein of thinking you also need to know what you need too. Do you need more sleep? Do you need more understanding? What about changing the diet a bit, or figuring out how Mommy gets calm? Do you need to wake up a bit earlier to read a book for a bit before the day's craziness starts? Maybe you need to answer fewer phone calls and have some time appreciating the wonderful time of life you are in. I suggest keeping a journal. Do it for your child right now. All day long look for the moments you don't want to forget and then right them in the book each night. Plan right now that one day you will give this book to her and that you will want her to see how much you enjoyed raising her. Make yourself look for ways to appreciate your motherhood journey.
About the tantrum behavior itself. My book has chapters on The Four Basic Skills, Time-out, Correcting Bad Behaviors, and The Rule of Three. These will be very helpful to you. If you can teach your daughter to follow instructions and accepting no answers, and you work on praising her when she does, then you will have more positive interactions each day than negative and your outlook on motherhood will change.
If my three year old were having tantrums then I would wait for a time when no tantrums were happening and teach the Four Basic Skills. I would have fun learning them and praise all the practicing and skill mastery while it was happening. Then I would tell my child that I would take her to time-out every time she didn't do these things. On time-out she will get the opportunity to calm down and be ready to be taught the right way to handle the situation.
As soon as she becomes calm I would come into the area and give her a big hug or high five and do an effective correcting teaching including practice of the appropriate behavior. I would praise the practicing and then give her a small chore which she could do, like picking up books or putting clothes away. The chore is the negative consequence, not the time-out.
None of this needs to hurt to teach her to change. It only needs to teach cause and effect.
When you take your little one to time-out: Do it the same way every time. Be calm. As soon as whining or bad behvior starts say, "You are whining" (or whatever the behavior is) and then gently walk her to time-out.
When she is ignoring you, she is still having a tantrum. She obviously has seen that these behaviors get her what she wants or at least helps her feel she is able to control you. So, don't let them happen anymore. If she can't get away with them, then she will soon stop. She could try to be more extreme first, but soon will stop power struggling because it is useless. Just remember to do it calmly and do the same thing every time. Also, make sure she knows you will handle the situation the same every time.