You're not alone in that. Pretty much everyone I've ever encountered who dislikes Pulaski as character... it's because all they remember of her is that first scene.

She's a great example of just how brutally important first-impressions are.

I definitely disagree that she wasn't her own, distinct character -- she was, I think you're letting that bad first impression continue to color your perspective. It's easy to misremember Pulaski as being abrasive and antagonistic because of that first scene, and hard to remember that she apologized very quickly after that, and very quickly became friends with Data (and remained very supportive of him throughout her time on the ship).

So it's weird seeing so much of the "discourse" on Pulaski boiling down to fans being angry at her for being mean to Data that one time while conveniently forgetting that she was one of only two people on that whole ship who went out and befriended the Android.