Help from other parents with young teenagers?

I think your issue lies in the statement “we give her as much as I can”...  That statement right there tells me that you have been a big reason for her entitlement mentality. Have you ever made her work for something and pay for something herself? Do you tell her no and make sure she understands to be grateful for the things she does have? I have two teens (15&13), and while they certainly have more than their father or I did at their ages, they are generally grateful for what they do have. We don’t give them everything we can, and they have to earn things and pay for things they want that we will not. 

Yes, some of this is normal, and if you react to it, you encourage it to continue. Like with the house shopping. She has no right to demand anything, and you need to make it clear that unless she is paying the mortgage, she may have an opinion, but you have the right to ignore it. When she throws her fit, stomps off and slams the bedroom door, you take the door off the hinges for a week as a consequence. If you don’t start taking a hardline, your tween brat is going to be a full blown teen monster.

You need to teach her that she can't always have what she wants in life first of all. For example tell her that if she wants to go to a water theme park then she needs to earn enough money to pay for it herself and you should also talk to her about how much these things cost. Yeah you've definitely created something because this sounds like you're giving her everything that she wants all the time. If she slams the door then you need to take it off It's hinges until she apologizes for slamming it.

Next time she demands something more than what is offered her, take away what is offered. If she is the smart girl you describe her to be, she will catch on to this idea that demanding more is met with punishment and to avoid punishment she will be thankful for what is offered.

She's spoiled

You tell her if she wants to go over seas then she has to pay for it 

Nothing she gets is good enough due to her being spoiled, take everything away and I mean everything but the bed, what clothing you allow and anything she needs for school work. No TV, no computer, no cell phone, nothing like that. She has to EARN those things 

If she wants to go to an expensive water park then she has to pay for it. If she whines about it then she can't go to the local swimming center

Tell her is she wants a larger bed room then she has to pay for it. 

Since she slams the door you take the door away and don't give it back 

Normal enough for a kid that'll be a nightmare teen if you don't nip it in the bud. Maybe she has a friend or a couple friends that go overseas on holidays and have big houses and that's why she's being difficult. But it's best if you let her know the reality of your situation financially.

Honestly she may be a bit young to understand fully just yet. But the earlier you start her on what you can and can't do with the money you have, the better off she'll be in the future when she has to provide for herself or starts working. She'll know how to budget her money and stuff. She's only 2 years off the legal working age, if she knows how to manage money by then she'll be far better off than the other kids who'll piss their money away on junk and alcohol and what not.

Schools don't teach this kind of stuff. She's gotta learn it off of you.