Why is my 11 year old sister such a spoiled brat?

Ok so it was my younger sister's eleventh birthday today. Her mom and dad are divorced but our mom still got her A LOT for her special bday. First she went to summer camp. Then she went to tutoring. Then we all went out to dinner at Denny's. She picked what she wanted and said she enjoyed it. We then went to the grocery store to get food. She did not get a birthday cake today because my mom likes to make her own cake (not buy a store-bought one). I know it is not the same to have a birthday cake after your real birthday but still... we still celebrated it! Then we we got home, she got about $100 worth of doo-dads like $20 worth of neon and tye-dyed socks, bff necklace from claire's, tshirt from target, headbands (claire's-neon and black and white with bows) and etc. All girl stuff that she liked. She had this "this-is-it" kind of face after it. We waited 10 minutes and then gave her the grand finale of multi-colored Coach shoes (brand new). These shoes were $90 plus tax which was $100! Yeah a $100 pair of Coach shoes for an 11 year old. Her response was "Wow!" She asked me, "should i cry?" She did not even say thank you to her mom! I mean seriously, if you just received a really expensive and nice present, wouldn't you say "thank you" immediately without "waiting." I had to tell her to say it. All she said was "thanks" with that pathetic voice. I looked at her disgustedly after that. She then was pouting all night afterwards. I asked her why she is so depressed and she said that we were yelling at her (her conseption of "yelling" is skewed because we did not yell at her. We simply takled to her in a normal tone of voice. She always thinks that we yell at her when we tell her something that she doesn't want to hear like she she was wrong.) I told her that I did not "yell" at her and she then had to start crying so dramatically. She then went in her room. Later I was on the computer. She came to me and told me to get off the computer because I am not allowed to..whatever. I was kinda annoyed with her acting like she is my boss. Meanwhile she said that she was going to rip my picture that I drew for her. I spent over one hour drawing and coloring her a hand-drawn "Ed hardy" resemblance picture with her name instead of "ed hardy". She of course crimpled it and later ripped it. I w as pist off because I spent a long time drawing that and I thought it looked really nice. That was art and can not be replicated. So anyways, she comes out of her room and tells me off. She blames me for "ruining her birthday." I tolde her that she got all the presents and that she was the one who couldnt say thank you to her mom. I am so annoyed with the way kids act these days. They do not understand how grateful they really are! $200 is a lot for one person to get, especially considering that we are not rich or well-off (we are poor). She is a big brat and sulks whenever we tell her she misbehaves or that we are disappointed in her. Can anyone please help me overcome/deal with this stuck-up little girl? Thanks for listening to me!