I need advice with helping my 5yr old transition to baby!

Ok everyone, I need some major advice. I have a 5 year old daughter and a 4 week old daughter. When we brought baby home, everything was going great at first. My oldest wanted to help and her mood had not really changed. I try to still spend one on one time with her when baby is asleep or in her swing, etc. But here the last 2 weeks, my oldest's attitude towards me has changed for the worse. She is constantly arguing with me over any and everything, She throws a fit over everything as well, for instance, I was going to put her in blue jeans the other day and she wanted to wear a skirt, so I let her. Then she threw a fit that she wasn't wearing blue jeans. She throws a fit if she hears the word no or stop for anything. She never used to do that much. But the tantrums I can handle when its just crying and such, however, hers are not. She is now starting to say that she wants to live in a different house, or she wants to run away, or that I hate her or don't like her, etc. It kills me everytime she says these things. I try so hard to make her feel not left out but its like she doesn't want me paying any attention to the baby. Might I add she loves the baby, and she isn't like that with her dad. Any of you ever had to deal with it to this extreme and is this normal. I knew there would be a transition time but I didn't expect this. I feel like I am a horrible mom and that I am failing in some way, but I do not know what else to do to show her that she is not loved any less.

I have tried talking, ignoring, timeout, sent to the room, toys taken away but nothing is changing it. I don't really see how I can spend more alone time with her than I do. I spend as much as I possibly can with a newborn that breastfeeds.

Any ideas on what to do, or has anyone went through similar situations? Does it get better?