I am a working mother. My daughter is 3 year old, adorable kid. She starts her day with a smile on face and then almost everything goes wrong. The moment she sees toothbrush she starts crying... from then on to almost every daily chore she whines. I specially dread the dinner time... She pushes away the food. She refuses to eat. Then I keep cajoling her to eat a bit of whatever she likes... This is getting quite stressful :( .

Hey.. I had four children,all were totally different in temperament.. I would say my middle daughter was a beautiful hound of a child who broke my heart from day one! Would not sleep,eat and sulked from dawn till dusk,however she is now 16 and a bundle of teenage joy!
You not alone in this,first don't make meals an issues,if she is healthy and active she will eat,if she won't ate a full meal at one sitting you could try offering her smaller meals throughout the day,also I found a reward system in the form of a star chart useful,example if she eats some fruit she gets a star,brushes her teeth she gets a star..
3 year olds are very smart little people and if she can get your attention by not eating or complying,its still attention. 3 year olds want attention!
Its hard when your working and running a household to keep all the balls in the air,but if you can try to encourage positive behavior and limited your reaction to 'bad' behavior,she will quickly learn she can get your attention by being 'good'.
As I said 3 year olds are smart little people and she will grow out of it..
There are loads of mothers on this site who will give you lots of good tips and advice,hang in there.

As for eating, I have this battle with my 2-yr old son several nights out of the week. One thing my pediatrician told me is that he won't starve himself. He will eat when he's hungry and stop when he's had enough. Some nights my son only wants applesauce for dinner. So if she doesn't want to eat dinner don't force it. It's hard sometimes to think of them possibly going to bed hungry but toddlers are strong-willed little people.

As for the other things, try Positive reinforcement. Praise the good behavior rather than focusing on the negative. I understand that sometimes the beautiful little creatures we created can test our patience to the absolute outer limits but sometimes you just have to walk away. Figuratively and maybe even literally. Choose your battles. Make sure to stand your ground on the important things like brushing teeth but don't get into a battle if she only wants yogurt for dinner.