Take another look at the original sentence:
You wanted to fix it this way:
A comma splice occurs when you have two complete sentences joined with just a comma. Sandra spent every dime on her vacation ... begins the first sentence. She doesn't care ... starts the second sentence. The addition of the conjunctive adverb nevertheless doesn't alter the fact that you still have two complete sentences joined with a comma alone.
You might want to consult the rules for fixing comma splices and fused sentences.