To be honest, this doesn't sound like a materialistic problem. She sounds down right bipolar. The symptoms you are describing (pushing you away, then pulling you closer again) are actually symptoms of a couple of mental health issues, like Borderline Disorder and Bipolar Disorder.
Sometimes, when people start dating, they can really "cover up" mental health issues.. but eventually (usually about 3 to 6 months down the road, sometimes longer or shorter) they will rear their heads. Since you've only been dating about 5 months, I sort of wonder if perhaps she struggles with something mentally of this nature that's only now becoming apparent.
The fact that her dad does something similar, is actually a tell-tale sign as well. Mental health issues can be passed down from the parents, not always biologically (though sometimes it is chemical), but through actions. You are correct when you say she may have "learned" to act this way. Never the less, this could be a part of her that is only now becoming known to you, and you need to be careful to realize it may be a part of her that is not temporary.
To answer your question: NO. A little promise ring should not be causing this much pain. Her actions are impatient, desperate (to "lock in" your promise asap as if you are going to run away), insecure (see the "desperate" brackets), juvenile, and down right concerning.
And frankly, I don't think you should be promising her anything with those kinds of traits appearing. You need to just slow down. Proceed with caution is really the only thing I can tell you. While this could be nothing at all? It could actually be a symptom of something huge. I'm not saying you can't date someone who might have a mental health issue (I have mental health issues, I married just fine) but it's something you need to be prepared for if it exists before you make any promises.