I would say she is in the wrong but you are also overeacting. She started the hostilities, so to speak, and now you see everything she does in a bad light.
Being upset at your dad about not being engaged: That's between him and her. There's nothing wrong with her feeling that way but they should have left you out of it. You don't air someone's relationship issues to his own daughter FFS! That's crossing the line big time.
Wanting May 29th: Again, totally appropriate on their part. I'm all for saying that brides and grooms only get a day but really, the day after the date you wanted??? That's crossing the line even more. Plus she didn't even stayed with that date (but not for you) so clearly, they didn't even want it that much to start with. It was very gracious of you to move your own date.
Your bridal shower: Honestly, I can see why they would be upset by this. You could have looked into doing it the next day or prolong your stay by a day if need be. That being said, if that the way that works with your budget and schedule, that's the way it works. They lost the right to complain when they planned on getting married a day after you and you have already given enough on the 'change your date front'. You don't have to accomodate them if you can't comfortably do so.
Their wedding budget: It's their money and their wedding. They have earned or saved it and get to spend it however they see fit. It's also not surprising for an older money to have more to spend. You are just being jealous and petty here.
Your wedding budget: They don't owe a penny. You are an adult, you are choosing to get married and throw a party for it; if people volunteer to contribute, good. If not, it's your responsibility. Likewise for not doing a honeymoon, that's not on them to pay for your vacations. You come out as entitled here.
Bridal party: Again, it is her wedding and therefore her bridal party. She chose to invite you and your sister to be part of it, a nice gesture, but that doesn't entitle you to dictate who is going to be MOH. Honestly, the fact that you would consider the mere presence of another person special to her heart as something that takes away from you is self-centered. That day isn't about you and someone else presence doesn't detract from you being a bridesmaid. Were you planning on making her your MOH?
In all that, I do think that her faults are waaaaay worse and I can completely understand that it colors how you view her every move. She has poisonned the well.