Sentences 1 and 2 are both problematic.
The grammar of Sentence 1 is faulty because the phrase “their daughters suitors” is in the wrong case; for the sentence to make sense, that phrase should be corrected to the possessive form “their daughter’s suitors” such that the sentence will read as follows: “Parents should not choose their daughter’s suitors.” Even in this corrected form, however, the sentence is flawed semantically. It yields the wrong, illogical sense that what’s being frowned upon is the practice of parents to look for men to court their daughter; indeed, I really don’t know of any culture anywhere that has this practice or custom. What I know is that in the normal course of things, a woman of marriageable age will attract any number of suitors, and that in some societies, for better or for worse, parents exercise a strong hand in selecting who among them is best suited for their daughter. To capture the correct sense for this state of affairs, however, the revised sentence needs to be further revised to this form: “Parents should not choose from among their daughter’s suitors.” The operative phrase that captures the intended sense for that sentence is “from among”; without it, the semantics of the sentence goes askew.
Sentence 2, “Parents should not choose for their daughters suitors,” is faulty both grammatically and semantically. Like Sentence 2, the phrase “their daughters suitors” is in the wrong case and should be corrected to the possessive form “their daughter’s suitors.” Worse, it misuses the preposition “for,” making the syntax of the sentence faulty. As already demonstrated for Sentence 1, the grammatically and semantically correct construction for Sentence 2 is also this: “Parents should not choose from among their daughter’s suitors.”
I would go further to suggest that to make the intended sense for Sentences 1 and 2 even clearer, we should add a clarifying parallel clause to that sentence as follows: “Parents should not choose from among their daughter’s suitors; they should allow their daughter to make that choice herself.”
Now, as to Sentences 3 and 4, they are constructed differently but actually mean the same thing.
In Sentence 3, “He appointed her US Secretary of State,” the phrase “US Secretary of State” functions as a noun complement modifying the direct object “her” of the verb “appointed.” On the other hand, in sentence 4, “He appointed her as US Secretary of State,” the prepositional phrase “as US Secretary of State” does that same job of modifying the direct object “her.” The sense of both Sentence 3 and Sentence 4 is precisely the same.
Come to think of it, though, I’d prefer using Sentence 4—the version using the prepositional phrase “as US Secretary of State”—because its meaning won’t become ambiguous when the gender of the doer of the action in the sentence is changed.
See how the semantics of Sentence 3 gets muddled up when the doer of the action is changed from the masculine “he” to the feminine “she”: “She appointed her US Secretary of State.” This time, the possessive pronoun “her” can logically be construed as referring to the subject (and doer of the action) “she” herself, such that the whole noun phrase “her US Secretary of State” becomes the direct object of the verb “appointed.” We now have a situation where there’s no way of knowing who was appointed as “US Secretary of State,” particularly as to whether the appointee is male or female.
In contrast, Sentence 4 makes the identity and gender of the appointee unmistakably clear: “She appointed her as US Secretary of State.” In this construction, “she” and “her” refer to two different women.”
To avoid confusing our readers, we should be on the lookout for such differences in nuance when constructing our sentences.
