Basically what you have to do to disqualify the employee from unemployment is prove misconduct. Insubordination can be considered misconduct which, “is a substantial breach by the employee of an important duty or obligation owed to the employer, willful or wanton in character, and tending to injure the employer”.
The test for misconduct is essentially volitional. “The conduct may be harmful to the employer’s interests and justify the employee’s discharge; nevertheless, it evokes the disqualification for unemployment insurance benefits only if it is willful, wanton or equally culpable.” It can be shown by presenting, “An employee’s deliberate disobedience of a lawful and reasonable instruction of the employer, related to the employer’s business, is misconduct”. You do this by presenting evidence of disciplinary actions, write-ups, and offer oral testimony (from HR, co-workers, or other personnel) to show that the employee willfully violated company protocol as delineated in written policies and/or handbooks.
What you'll want to do do is explain in detail the insubordination and provide if possible any and all documents that show a) the rule, b) the write ups or notes from meetings held, c) an explanation of the number of times and or warnings about such acts, and finally d) the final decision in writing. Now if the employer doesn't keep these records really all you have to rely on is your witnesses there - the boss, co-workers managers - they should put together statements to submit as proof. It's a lot to work to do, but if you go to hearing on it you'll need something to present in anyway.