I'm sorry to hear of your loss. As other people have said you need to read the definition on your policy as to what is classed as an relative. All policies are different, and in a lot of cases you get what you pay for. If it doesn't state that it includes your cousin then you won't be able to claim.
As an alternative you could try writing to the travel company and appealing to their better nature (if they have one), focusing on how much you were looking forward to your holiday, your disappointment with the insurance and the trouble it is causing you at this difficult time, and that you would expect more from reputable companies such as this, and that there will be no chance of repeat business from you or anyone that you know, or words to that effect.
You might find that they will offer you something as compensation in order to protect their reputation, but i doubt you will get a refund though. Hope this helps.