While you have your hands full with a baby and full-time work, arguing with a smart four year old girl is your biggest mistake. How can you WIN with her D.?
What I mean by this is: how can BOTH of you win every "battle" instead of just you or her?
It's time to think outside the box here. What is your tone of voice when you ask her for something? How do you reward her for good behavior? How do you punish her when you are not happy with the outcome?
HOW MUCH HAVE THESE THINGS CHANGED SINCE THE BABY WAS BORN?
A new baby in the house means competition and frustration for a four year old girl. She needs a way to express her anger and frustration and is obviously doing it well. You need to catch on - she isn't arguing with you D., she is asking you to LOVE HER TOO, like you do her baby brother.
So, calm down. Use a gentle tone of voice - the same voice you use with her brother. Ask nicely and don't yell when she says "no" - she needs to say "no" right now, she is mad at you. The less you get mad back the less she'll argue with you.
Think like a four year old D.. She is still a baby too! Talk to her with a gentle, loving voice... cuddle her and tell her that you love her EVEN when she says "no". Tell her that her baby brother has NOT replaced her in your heart.
You two have some healing to do - and believe me, it will take a lifetime to heal the wound of breaking up a great twosome like you and her (ask any mom who has had a second child). She'll be mad about this her whole life... so don't add to it.
Remember, she was your ONLY baby just 6 months ago. But she needs to be reminded every day and every minute that she will always be your one true love (even though it's not true).
When you get some extra time, go to the bookstore and pick up: Raising Your Spirited Child by MS Kurckina. A daughter this smart needs a good OWNERS MANUAL. This is the book - you won't regret reading it on your lunch break today.