I know that you are supposed to separate dependent clauses and introductory phrases with a comma if they start the sentence. Examples:
If you are ill, you ought to see a doctor. (dependent clause)
After the adjustment for inflation, real wages have decreased while corporate profits have grown. (introductory phrase)
However, the above reference does not give examples of punctuating compound and complex-compound sentences that include dependent clauses and introductory phrases in the second part of the sentence.
Example of such a sentence with original punctuation kept (I took it from Wiktionary — an example of usage for word particular in sixth definition):
He is very particular about his food and if it isn't cooked to perfection he will send it back.
I think that there should be a comma after the word food, but that is not my question.
My question is if there should be a comma after the word perfection.
Similarly, sould there be a comma after an introductory phrase which comes after the first indepedent clause but before the second indepedent clause? (Although it is probably considered to be a part of that second independent clause.)
[independent clause], + coordinating conjunction + [introductiory phrase] + [independent clause].
Comma or no comma after an introductory phrase in the above structure?