Independent clause + comma + and + dependent clause + comma + independent clause

Your first comma separates two independent clauses. Thus, it is correct. The second comma has nothing to do with that.

First of all, my question is about the first comma, not the second comma.

Second of all, "if she has a backache" is a dependent clause, not an independent clause.

donnach said:

I think of "if she has a backache, she will take medication" as something like a unit, which is why it can take a "comma plus and" to separate main from dependent clause--because the main clause is following right behind the dependent clause.

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I agree.

Another justification for the correct placing of the comma, is that if two commas are used parenthetically, as they are here, the phrase within them should be able to be deleted and still leave a grammatically correct sentence.
With "She is certain about it, and if she has a backache, she will take medication.", this doesn't happen.

"Comma style has changed over time, and probably will continue to."
"Comma style has changed over time and, at least as I see it, probably will continue to." OR
"Comma style has changed over time, and, at least as I see it, probably will continue to." This is probably most correct, but, as with full stops, the number of commas used is possibly decreasing.

donnach said:

First of all, my question is about the first comma, not the second comma.

Second of all, "if she has a backache" is a dependent clause, not an independent clause.

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But the second independent clause does not end with "backache". There is more to the sentence.