Conjunction Puzzle: Is this clause dependent or independent?

Solution 1:

It depends on your teaching purpose. Notwithstanding Pitarou's comments and link about FANBOYS, it may well be appropriate for third graders to learn that sentences whose two clauses are connected by one of the FANBOYS (coordinating conjunctions) are called compound sentences. Sentences whose two clauses are joined by one of the other (subordinating) conjunctions are called complex sentences.

Hence in your list sentences 1 and 3 are compound, and sentence 4 is complex. Sentence 2 is somewhat problematic, since therefore is an adverb and some strict grammarians would object to it being used to join clauses thereby producing a run-on or comma splice.

Solution 2:

You are quite reasonably worried about edge cases.  Before we look at them, let's look at some much simpler cases.

I like spaghetti and Bob enjoys macaroni.

This is very clearly a compound sentence.  "I like spaghetti" is one clause, and "Bob enjoys macaroni" is another.  Neither clause does any work to or in or for the other.  They are independent, coordinate clauses. 

I like spaghetti when I'm feeling sad.

This is very clearly a complex sentence.  "When I'm feeling sad" is a complete clause with its own subject and predicate.  This clause is inside the matrix clause and it does work to the verb "like".  In this case, it does the same kind of work that an ordinary adverb can do:  "I often like spaghetti."

When I was in grade school and high school, FANBOYS wasn't a thing -- at least, it wasn't a thing that reached me.  The main coordinating conjunctions were "and", "but" and "or".  Occasionally "nor" would pop up without a matching "neither".

The nice thing about this small, tight group is that they can coordinate, oh, nearly anything.  Even simple nouns and pronouns can be coordinated: 

Bob and I like pasta.  -->  Bob likes pasta and I like pasta, too. 

We eat spaghetti or macaroni every Tuesday.  -->  Every Tuesday, we eat spaghetti or we eat macaroni. 

Nobody but Bob cooks pasta in a microwave.  -->  Nobody else cooks pasta in the microwave, but Bob does.

Coordination works the same regardless of the scale.  I can't think of any examples where "for", "so" or "yet" coordinate a pair of nouns or pronouns.  Until I see a good example of something like that, I can't consider them to be coordinating conjunctions.

With that in mind, let's examine your sentences: 

All dogs are mammals, so huskies are mammals.
All dogs are mammals, therefore huskies are mammals.

I don't see either coordination or subordination here.  I see a pair of run-on sentences.  As I interpret them, "so" is an adverb with a meaning similar to "in that fashion" or "as a consequence", and "therefore" is an adverb with a meaning similar to "for that reason" or "as a consequence".  Back in my day, such comma splices were simply considered as errors.

All dogs are mammals.  So, huskies are mammals. 
All dogs are mammals.  Therefore, huskies are mammals. 

I come bearing soup, for Kate is sick.
I come bearing soup because Kate is sick.

In this pair, I do see subordination.  The subordinate clauses do the same job that an adverb would do.  Specifically, the clauses act as adverbs of reason or purpose.

If I were you, I'd ignore FANBOYS entirely.  I'd still teach coordination and subordination.  I'd teach coordination first, from words (Bob and I) through phrases (over the river and through the woods) to full clauses.  I'd then teach subordination by showing how an entire clause can do the same sort of job inside another clause that a single word can do.  The point of having subordinate clauses is making them do the work of nouns, adjective and adverbs.

And there's your meaningful difference.  Coordination means two things working together to do the same job.  Subordination means one thing doing a job for another thing.