The sentence is ungrammatical and meaningless
I would assume that the middle part is some kind of parenthetical phrase giving some extra but unnecessary information and is probably understood not to mean "if" in the formal logical meaning but is an error for "not because". But infering this as an error is difficult because usually I would be guided by common sense to understand the meaning. Your sentence has no common sense.
The form "not if" should be used with negative main clauses:
I will not go to school today, not if the Principal himself tells me to.
Logically the "if" part here adds no meaning, since "I will not go to school today" logically means "under any condition". Specifying a condition like this means "If the principal tells me to then I will not go to school & If the Principal does not tell me to, I will not go to school". So logically it adds not meaning and is of rhetorical use only.
Your sentence, therefore, is ungrammatical. As the meaning is so odd I can't guess the intended meaning pragmatically. As a result, the sentence is meaningless.
A grammatical sentence could be
I will go to school today, not because it is snowing, but because my cat is awake.
Here the final clause modifies the first, and the middle one is clearly parenthetical.