I know Sorry got that when I read it second time around!!

I think it comes down to you get what you pay for.

I have multiple pets insured with Animal Friends Insurance and have found them really good - paying out promptly. I have been turned down for one claim which I appealed against and it was reinstated. I have also appealed against an exclusion which was denied. This is reasonable cover from the cheaper end of the market and they keep the prices down by us having to pay a larger proportion of each claim. I dont think they are any different from any other insurance company.
However (and I havent read all the posts) I would appeal in this case as this sounds like exceptional circumstances and it is worth a try. You need to get someone who knows a bit about insurance to help you write the letter and maybe evidence it with photos of the wall etc.

Hope you and your lovely dog are beginning to get over this dreaful business.

Thalice's Mum