The normal tourist visa is 14 days long. They can get it at the airport for 15$. I wouldn't recommend bringing a dog that far only to turn around and fly it back again 2 weeks later, not only is it very very hard on the animal (we are talking at least 24 hours in transit), but its not very cheap, because Britain will not allow animals threw because of bird flu which means the dog will have to fly sepratly in cargo to Amsterdam. Please try to convince your mother NOT to bring the dog. I've flown my cat one way from Korea to Canada, Canada to the Middle East and it took her a month to adjust.