"she’s hinted that she wants something but won’t tell me what it is and she said that if I wasn’t to get her this item then it wouldn’t show her how well I knew her and how little I cared. "
RED FLAG, dude.
She's baiting you into a trap. This is manipulation at worst, and naive and unfair at best.
You guys communicate like shiiiiit. Whether you intend to marry or just be together long-term without marriage, your relationship CANNOT continue with situations such as this happening. It's going to lead to arguments and hurt feelings. And, again, if she makes a habit of pulling stunts like this to have you "prove" how much you love her or how well you know her, then that's actually a form of abuse.
You need to sit her down and say, "Look, honey, I want to get you a nice birthday present. If you want something specific then you need to tell me what it is and I'll be happy to get it for you. If you'd rather be surprised, that's fine, but then you can't hold it over my head if I cannot magically guess what it is you're hoping for. We need to communicate better, so you need to tell me exactly what you are hoping for her - either a specific gift or a surprise of my choosing - so there are in hurt feelings later on."
If she refuses to do this, then personally I'd run for the hills, because if you stick around with a partner like this then you're in for a lifetime of headache. It's unfair and mean of her to just flat-out tell you that you need to "prove" yourself to her and she's going to get pissed at you if you cannot magically guess what gift she's thinking of for herself.
Also, I would NOT rely on her daughter for information about what she wants. ASK HER YOURSELF. Don't take a third party's word as truth. You have no idea whether your GF told her daughter to hint around to you (which is immature and stupid), or if the daughter is taking it upon herself to guess what her mom wants.
Also, don't buy a promise ring just because someone else told you to. Especially since you apparently have no idea what the fuccckkkk a promise ring even means or what kind of promise you're supposed to be making to your partner.
And ditto those who said that, if she IS hoping for a promise ring, it's (a) really immature and stupid because promise rings are something that teenagers in 50s movies do, not real adults; and (b) she could be very well manipulating you into an engagement, which you've said you don't want. Again, COMMUNICATE with each other, it's not that hard.
Your priorities are all kinds of fuccckkked up, and your girlfriend sounds like a terrible manipulator. I'm glad to hear you guys have no plans to marry because your relationship sounds absolutely awful right now. And, again, you clearly cannot communicate for shiiiiittt.
Forget about the stupid birthday present right now. Instead, sit down with her and have a frank conversation about communication, expectations, honesty and fairness. Otherwise, you may as well just cut to the chase and break up now, rather than enduring years of immature petty bullshiiiiiit from each other before it inevitably happens down the line.