Does the if clause modify "I will play the violin" even though the clauses are not next to each other?

I will play the violin when I am at the park if my fingers are not sore today.

Is the "if" clause modifying "I will play the violin" even though these clauses are not next to each other?

So that the sentence means:

If my fingers are not sore today, I will play the violin when I am at the park.

I know using an "and" between both subordinate clauses would clear up the confusion, however, if there is no "and" does a "nesting" situation arise?