Claimed with VHI for stolen camera last year, easy to deal with - I didnt have a police report, just called them straight after it happened. However, did try to claim for a cancelled flight / overnight stay etc and they wouldn't pay out - maintained that only my outward and inward leg flights were covered, not any other flights while I was away. So my flight between China and Thailand didnt count!
Not sure what their payout policy is in relation to cancellation - close relative is usually spouse / common partner, grandparents, parents, parents in law, kids, daughter & in law, sons & in law. Have just checked the policy document and it states they pay out due to 'The death, imminent demise, or hospitalisation due to serious accident or unforeseen illness, of a Close Relative'. I suppose it depends on whether you can state you knew or didnt know of the situation when you booked. You ll need to know what exact charges you ll incur (some hotels may only charge for one night if cancelled a month before etc)