My girls are 4 years, three months apart, and I remember it very well. First of all, do NOT call the baby the "NEW" baby. It implies that she is now the "OLD" baby, and in her experience most old things get thrown away, or given to other people.. Am I right? She may think she is no longer as good as a "new" child and her anxiety is making her act out..
OK .. that said, let me tell you that 4 year olds are difficult people to live with... little sibling or not. I remember reading a book "Your 4 Year old; Friend or Foe" How true that is... They are on the brink of a HUGE developmental change. The difference between a four year old and a five year old is amazing. It will boggle your mind. So expect some regression, ( my daughter wanted to nurse, sit in the high chair, go back to a crib and wear diapers. But that's another topic LOL )..
To reduce her stress, try as hard as you can to keep things the way they were for her before her brother was born. Make her life feel secure with the routines she was used to. If you can, let someone else (husband, mom, etc) deal with the baby, while you bathe, read to, do bedtime, etc.. what ever you USED to do with her.
When you are with the baby, try to make sure that it is a special time for your daughter too. I used to have "story time" while I nursed her sister.. I made it clear that this was HER baby too, and I needed her help to make the baby feel like part of the family.. I'd ask her for her opinions. When visitors came to the house I told them before hand that their first question should not be about the baby, but about the Big Sister.
Tell dad to stop the gifts, keep the old routine, and make her feel special and proud with attention and praise. It's only been a week... give her a chance to adjust to her new life.. It is a crisis for her, and you have to be patient.