I love your proposed categories, and I agree with them quite a bit. However, I'm unsure of "Choose" being an appropriate substitute for "Care". Please correct me if I'm misunderstanding something, but I've always understood choice as involving some capacity to pick alternatives. While Autonomy would be preserving the capacity for choice in this respect, I think some of what we know about the other shards under this category either contradicts or does not follow this conception of choice. For example, take Odium's unmade. While Sja-anat would fall neatly under a subcategory of "choice" (chooses to disobey Odium, is driven by other wants), Nergaoul and Ashertmarn are both mindless (have no capacity for choosing alternatives) and one can only preserve his or her capacity for choice by resisting their influence (Veil in the Cult's party and Dalinar during the end of Oathbringer). "Care", while it doesn't fit quite well, wouldn't really pose any apparent contradiction here and would fit far better than "Choose".
What I'm a bit confused about though, is whether the influence of these shards is prior to or explanatory of the natures or actions of those they influence. I think I'm leaning towards the former. Dalinar's momentum caused him to act violently under Nergaoul's influence, but he didn't act to fulfill some sort of goal or desire that was created by Nergaoul. I'm not sure if this would apply to everything Odium or the other shards influence though. I think them being prior would also work better to further separate this category from "Change". If we consider this category as explanatory, then it would be complementing "Change" and would almost be meaningless without it. It would sort of translate to "The purpose behind changing". But that shouldn't always be the case. I think it's possible for someone to be possess a strong ambition or emotion without that emotion causing them to do something (for the lack of capacity to change, or overcoming these desires with rational thought). Yet we would still call these emotions there even when actions do not follow from them.
This makes me think that while the fourth category can influence actions and choices, it shouldn't be restricted to them.
I propose that the category should instead be "See". Except for maybe Autonomy, the other shards seem to heavily influence one's perception and cognition. I think if there were a Shard for reason or rationality, it would also fit under this category. I think this theory is supported a bit by how the Alethi and the Veden seem to perceive things very differently under the influence of the Thrill. You could also say the death rattles are an alteration of the perception of the near-dead. I also think you can similarly explain the influence of Sja-anat and Ashertmarn. If Devotion would influence religious faith, then you might use this to show how extreme religious fervor can cause people to perceive things very differently. I think maybe Autonomy could account for one's perception as being individual from the whole? But perhaps that might fit better as a negative under Unite.
I would then categorize them under the command of "See" as such:
See - External - Positive = Devotion
See - External - Negative = Ambition
See - Internal - Positive = Odium
See - Internal - Negative = (Reason/Rationality/Wisdom?)
I'm honestly unsure how to think of the Positive/Negative distinction. If it were a push/pull distinction, then I suppose Ambition and my placeholder for rationality (if it is indeed a shard) are pulling, while Devotion and Odium are pushing. But I'm really unsure about this.
But that's just how it all fit together in my head. Please tell me if you have any thoughts about this, and if you think I made any errors or disagree with how I approached my conclusion.