I think it's the combination of the two. Diana being a slightly more aware version of the Superbuddies take on Mary Marvel - an innocent sweetheart mystified and saddened by Fire's brattiness and the general inability of the Superbuddies to be friendly or responsible people, all "I don't get it, how can they act this way?" would... still probably not be *all* that funny, Mary's exaggeration only works because she's an ingenue, but it would at least be a legit parody of Wonder Woman. Perez' Diana really was too naive to live, and Jimenez played that disappointed dismay up too, so taking that over the top is definitely an angle you can take with the character.
Conversely, you could play her up as super-responsible and super-good to a point that's just silly. She's not mad, she's just disappointed, and she knows they can all do better, and that there's more to Bea than she's showing and she could be a good *example* to Mary and the boys, all uber-maternal in a way that aggravates the hell out of Bea and delights Mary (which also aggravates the hell out of Bea). And Diana understands that too and thinks that Bea should be better than that as well, and et cetera. That would also work, and be a natural and effective exaggeration-to-parody of the character.
When you try to do both at once, though, it's not "look this character can be taken to silly extremes" like everybody else in the cast anymore, it's "look, if we exaggerate wildly in two totally incompatible directions, this character becomes hypocritical, inconsistent and stupid, and aptly mocked by our other characters" and then you're on the Character-Bashing Badfic Failboat.