When our DD1 was younger, she was very fixated on shopping at every store she could see. NOT me - this definitely came from DH's side of the family! We've adjusted with our kids as they've come to understand how money works, but always worked at instilling a sense of budgeting and delayed gratification:
So when she was younger, we gave her a little coin purse and if she wanted to buy something, we'd tell her how many coins (pennies, usually, but we made no distinction) she had to pay and we would pay the rest. If the present was too big, or too expensive, we'd set the # of coins either to clean her out or even too expensive, or to leave her with very few coins to spend later. As she got older and got better at math, we went the gift card route. During this time, she was very into princess dresses, so we still say we will buy them each ONE princess dress, their choice of princess. And so since there's one princess dress already on the table as the *big* present from the parents, they also know not to expect anything more from us. (we usually do get additional things for them, but make it a surprise) Our DD1 (8) now makes pretty wise choices with her gift card, and values the things that she buys. I've expanded the things I will buy for her to also include a pin - she's more into pin collecting than trading, though. DD2 (almost 4) is still in the coin purse w coins stage.
3- Whatever they buy has to make it home on the plane. It either has to fit in their backpacks, or in the extra luggage space we have. (We usually take 3 1/2 full pieces of luggage with us so we have room for stuff on the flight home). This stops them from buying massively bulky items like the giant Stitch plush my daughter wants that I'd probably have to buy an extra airline seat to get home.
We have this rule too. Actually I loved your entire post. And when DD1 begged for the light up castle with fireworks, I took a picture of it and told her that I'd check in with her on her birthday and if she still wanted it, I would get it for her at home. I also sometimes send those pics to grandma so she has clear guidelines (and limits) for what to get the kids. That said, the rule went out the window the year DH and DD1 conspired to get a lightsaber that had to be hand carried on the plane. Then again, they got many years of enjoyment from it before it finally broke. (A battery corroded in it)