Hi, Ciera!
My kids are 12 and 9 and I find that by giving them a
Disney Gift Card in lieu of cash, they are much more careful about spending it, and they know exactly what their "budget" is for their vacation. If this card is simply for souvenirs, I find that $50 is usually a fair amount for my kids. With this, they can get a Vinylmation, a hat or T-shirt, and a few small miscellaneous items.
If this gift card is also for snacks (not meals) you might want to add on about $10 a day to that amount.
Take a picture of the back of your gift card (scratch off the PIN) in case the card is misplaced since this is like having cash. After each purchase, the card balance will be printed on your receipt.
I hope this helps! Have fun planning, your vacation will be here before you know it!