If I have no money but my friends are going shopping, I wouldn't have a problem going with them and do the window shopping.
But that's not the point here though. You wanted to go shopping so you went. She had a problem with that. I could understand if you invited a group of friends but not her but you didn't. I would ask her what the actual problem is here and go from them.
Next time don't make assumptions about what she would and wouldn't like to do - she may want to spend some time with you even if she has no money but give her the chance to make the decision by herself.
I think you didn't do anything wrong here.
I think your friend is being a little petty over this. :-/
If it is one of your best friends or sister then you should have invited her. If she is just a friend then you were considerate to not invited her to go shopping.
First of all you needed to buy some clothing and you look your LIFE PARTNER with you. She doesnt need to go with you ALL THE TIME. If you invited other friends to go shopping with you and you didn't invite her ...well that's a different story.
She is being ridiculous for being mad that you went shopping by yourself. If this is something you do together often I can see she might have her feelings hurt a little bit but any normal adult would keep that to themselves and understand that there was no obligation to invite you.
However, I strongly encourage you not jump to the conclusion that she is declining to go to Six Flags because she is still mad.
First, you have no idea how much her paycheck was or what her bills are. She MAY NOT have any extra money.
Second, even if she has extra money, she may not want to spend it at Six Flags.
Third, accompanying you shopping costs her nothing if she doesn't buy anything. Six Flags costs money no matter what. The two are completely unrelated.
Finally, it's possible she would have rather gone shopping (free) and spent time with you alone than go to Six Flags (expensive) and spend time with your family.
My best advice is to think about things from HER perspective before you get all bent out of shape. The last thing a friendship needs is TWO people acting like children.