You know, I think I feel sympathy for this girl because I'm not getting "bridezilla" vibes here; I think something else is going on under the surface. The following is assuming, of course, that what's in the story isn't a gross distortion on what actually happened (a risky bet, but what else can one do?).
The writer seems somehow to be very emotionally fragile. I get the sense that she's desperately tried to get her parents' approval, and never felt that she succeeded. Now, she's finished law school, she didn't get pregnant, she's found a husband, she's even "earned" a white dress - she's done everything a "good daughter" is supposed to do to make her parents proud of her. And what's their response? That she should have the least expensive, least effort-consuming wedding that's possible. I don't think she's really upset about a BWW (certainly $2000 isn't likely to achieve a big one) - I think she was hoping they were going to go, "Darling, we're so proud of you - of course we'll throw a wonderful wedding for you, so everyone else can see how proud we are as well". The money wouldn't be as important as a little bit of gushing. Even if they're stone broke they could make her feel appreciated, and I don't think she does feel it.
Now, it appears that they themselves weren't into spending time or money on their own wedding, so I doubt they're even aware of why she's really upset, and perhaps she doesn't know herself. I think she's emotionally needy, they're emotionally cold, and the two styles aren't mixing.