I have learned that "что" is not used as a relative to an animate noun antecedent. But I found a few sentences that do not follow this rule: "Эта сестра, что я всюду таскала за собой." "Сестра, что увяла подобно дивному цветку." (These are lines spoken by a heroine in a story. She is talking about her frail sister who has died.)
What is the difference between the above expressions and the ones in which "что" is replaced by "кого/кто" or "которую/которая"?
"Эта сестра, что я всюду таскала за собой."
\____________A______________/
Normally we don't speak the part A as of an animate. More to the point, because we're not linking the verb "таскать" to an animate as appropriate.
The next thing, if we substitute an animate object for a lifeless thing,
"Эта книга, что я всюду таскала за собой."
this sounds as a chaotic colloquial speech in a context where the speaker is a little lost, and has mixed feelings about something. This is the way to a correct expression of that. Literary and written Russian:
"Эта книга, которую я всюду таскала за собой." "Эта сестра, которую я всюду таскала за собой."
But your question is more about whether or not we can substitute the pronoun "что" for a living thing. it turns out, while the pronoun "кого" pointed out to an animate man-person, we don't have the counterpart for an animate woman-person. For example,
Этот брат, кого я всюду таскала за собой. (okay, given what we have said)
Это существо, что я всюду таскала за собой. (okay, too)
*Этот брат, что я всюду таскала за собой. (*Ungrammatical, there IS "кого")
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Logically, what is fair for a man-person could be applied to a woman-person, but as long as there is no counterpart to "кого", then it somehow became acceptable in conversation.
There is the way for literary and written Russian with "кого":
Это говоришь мне ты, кого я всюду таскала за собой? [:astounded](okay)
where "ты" can be a woman-person or man-person.
*Это говоришь мне ты, что я всюду таскала за собой? (Ungrammatical)
^^^_________________________________|
ungrammatical, because "что" pointed out to smth but "ты".
I have learned that "что" is not used as a relative to an animate noun antecedent. But I found a few sentences that do not follow this rule
And from these you may safely deduce that this rule is wrong.
What is the difference between the above expressions and the ones in which "что" is replaced by "кого/кто" or "которую/которая"?
The difference is that "что" here sounds bookish / outdated / poetic-alike. Normally people do not talk like this. But it's OK for a book.
UPD.
But I still want to get some idea how Russians imagine the speaker's psychological situation when they hear such expressions
As you see both sentences look the same. That is, "что" itself isn't about love or hate. It is rather used to mark the start of "a poetic description". And its repetitive use is, no doubt, an intentional anaphora.
