Can I also ask the court to modify the property division after the divorce has become final?

The only grounds for modifying a property division after the divorce is final are grounds relating to fraud, mutual mistake, failure to disclose property or debt, and similar issues.  Even then, a party has one year at the latest to file a motion to amend the judgment of divorce in most circumstances.  If a case has gone to trial and there is a judgment from the court, one option is to file a motion for reconsideration if the judgment is unacceptable.  The second option is an appeal to the Court of Appeals, which must be filed within 21 days of entry of the judgment.  Timing is everything.