You may be able to electric fence areas to provide what you describe, but goats can be tricky to train to electric as their instinct is to run through it when shocked. If you can train them to it you may do well, otherwise it will be very difficult to find anything that is goat proof and moveable!
Regarding insurance there are multiple companies doing farm/smallholding insurance that you can add some pet animals such as cats, dogs and horses to, depending on the company and policy. The nfu would be one, Stuart benger and fidelius also do similar policies. Have a chat with them all to find out which suits you best. Or petplan for cats, dogs and horses and another for farm animals.