Hi Grinnell. I'm a little hesitant to add to the discussion, as I am not a parent and my ideas/advice may or may not be feasible. So please feel free to accept or discard any of the below.
My thought is that, at 12 years old, your daughter is starting to form her independent sense of self that will carry her through adolescence to adult-hood. So maybe it's time to start treating her less like a child and more like a teen/young adult. What I mean by this is that instead of saying "no" all the time to her requests, turn it around on her so she can start learning problem-solving and money management skills. When she says she wants something, sit her down and encourage her to come up with ways to prioritize what she wants and get what she wants. Ask her leading questions such as, "How much does that item you want cost?" "Is there some place you can buy the same or similar item for less than retail price?" "What are some things you can do to earn the money you need to buy what you want?" The idea is to give her some kind of ownership over her challenges, and empower her to figure out things on her own (but with guidance from you). You're no longer saying, "No, you can't have that" all the time, but instead saying, "Let's see if you (or we) can figure out a way."
At 12, she's old enough to do certain jobs around the neighborhood like babysitting, paper route, mowing grass in the summer or shoveling snow in the winter. If you and her mother are so inclined, you could also offer her extra chores to do for extra allowance money. If she's not willing to work to buy the things she wants, that's her choice to make, which means that she now bears some responsibility for not getting things that she wants.