Comma usage before coordinating conjunction after a long clause

Question

It is correct to put a comma before a coordinating conjunction when the second clause is independent of the first, e.g.,

Sally picked apples, and she placed them in her basket.

but not if you remove the second "she", e.g.,

Sally picked apples and placed them in her basket.

(Here the second clause, "placed them in her basket" is dependent as it can't be a standalone sentence.)*

What if the first clause is lengthy? E.g.,

Sally picked apples to sell at the farmers' market, and placed them in her basket.

Here, I feel that avoiding the comma makes the sentence sound wrong, although I can't put my finger on why.

Also, if a comma is warranted in such a situation, how long is long enough?

Sally picked apples to sell and placed them in her basket.

Sally picked apples to sell at the world-renowned Nettleton Farmers' Market on Tuesday, and placed them in her basket.

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^{*See my answer regarding this error}

Answer 1

This construction is simply a compound predicate — picked and placed — with a single subject — she — not an independent clause joined to a dependent one — but more on that later.

We baked a cherry pie and left it on the counter to cool.

The rule that a comma should not separate the elements of a compound predicate, no matter how many intervening words, is not controversial.

The longer the sentence, however, the greater the temptation to insert a comma. I suspect it's because the sentence is analyzed as two independent clauses where the second has an understood (or elided) subject, much as you are attempting.

Sally picked apples to sell at the world-renowned Nettleton Farmers' Market on Tuesday, and she priced them accordingly.

If the subject is expressed, then the comma is correct; make the subject implicit and the comma should ostensibly disappear.

I have seen countless sentences of this nature — also from careful writers — where a comma is used but the subject is not restated, so I suppose it's just a matter of time before it's considered correct.

Answer 2

A note on my confusion between a dependent clause and a predicate

Sally picked apples and placed them in her basket.

Here, "placed them in her basket" is not a dependent clause, as I originally thought, but a predicate. A clause contains a subject and a predicate, but "placed them in her basket" does not contain the subject; it is just the predicate. I thought it was a dependent clause because it cannot be a standalone sentence (which it can't), but that doesn't matter because it doesn't fulfil the requirements for being a clause, never mind independent or dependent, in the first place.

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As the Wikipedia link explains, the traditionalist view of the whole compound predicate would be (in bold)

Sally picked apples and placed them in her basket.

"placed them in her basket" is one part of the compound predicate.

A more recent view is that the predicate is

Sally picked apples and placed them in her basket.

In this view, predicates are like mathematical functions that take subjects and/or objects as arguments/parameters:

picked(Sally, apples)
placed_in(Sally, them/apples, her_basket)

The preposition "in" is part of the second predicate. The coordinating conjunction "and" joins the two predicates.