Focus on the big picture. The only times I remember Hinata being of note in Part 2 are the chapter of her introduction, her confession chapter and those three you mentioned. That's a grand total of 5 chapters in which she actually mattered.
Her involvement in the Itachi arc is nearly forgettable since she wasn't connected to the plot. She was just there to assist as a background character.
The you have Karin being essential in the pursuit of Itachi and evasion of Konoha, you have her assisting Sasuke in the fight against Killer Bee, and you have her dealing with Sasuke's darkness in the Summit arc. That's a lot of relevance in a lot of chapters.
God I cannot believe I did not notice this,
Karin is actually more important than HinataShe has had active involvement, generally around Sasuke, but this goes across the Itachi pursuit arc to the invasion of pain to the 5 kage summit and now her reunion with taka. She has had an active involvement even if she purely was on the sidelines. I mean Sakura does fight in a bit minor roles for most battles, but Karin is just a sensor and medic. Sakura is a fighter and medic. Yet What has Hinata done of importance? Get blasted in the face twice and lose her cooler well developed cousin.
Its like if Sakura ended up defending Naruto in the next few chapters but gets gravely injured (I don't believe she would die, if she died it would ruin a lot of the story.) The majority of fans would go "Haha serves you right you pink haired *****." Yet with Hinata, they go "Aww she got stabbed though the abdomen again, that must be love." Before 615, they claimed Hinata would never hit Naruto on purpose, yet she does in 615 and they become double standard boot lickers again. This whole mental gymnastics stuff really gets tiresome.
If we want to go by prominent active female characters in order, I think it would be like this:
1. Sakura - as she is the heroine she has the most screentime
2. Tsunade - she is the hokage, she has a constant reoccurring but also takes some active roles like in her intro arc, pain, and obviously the war.
3. Ino - not as enduring but she did get a major arc with team 10 and that part in the war arc when facing edo Asuma with Shikamaru and Choji.
4. Shizune - generally follows Tsunade around and only has a comment or two but she appears more than most others and yet has less importance in the story aside from being Tsuande's aid.
5. Karin- She was around heavily at the start of the Itachi pursuit but still had present roles with the killer bee fight and her betrayal at the 5 kage summit.
6. Hinata- now we have Hinata, she takes a backseat to all these other ladies. Her only arc of having a significant role is still the chunin exams, after Naruto pummels Neji, her importance in part 1 ends. In part 2 she makes a minor reappearance and does nothing until pain. Then another 4 years until 615. Even for her major moments, they are minimal, they just literally come forward once every 100 chapters. Even then, because her first reappearance towards Naruto was only her reintro, that does not count for development. Literally from her ending role in the chunin exams until pain, hinata does nothing for the story. 332 chapters of nothing. This is supposed to be important? Thats practically half the series. NH fans think that this big gap can be erased, it cannot. Yeah she was around in the Itachi pursuit but that arc was focused on Sasuke and Itachi, Naruto, Sakura, Kakashi, and everyone else had no real development that arc. Hinata literally spends most of her time in the crowd.
7. Tenten- her roles are minimal and battles are offscreen. She has had some activity in the kazekage rescue arc but TenTen is practically non-existent.
8. Temari- she is only important when Gaara is around. Even then it is a highly rare to see Temari.
So this is as I see with the reoccurring females most with constant activity in the manga. Sakura at the top (no suprise here) and Temari at the back.