Can't help with the DR-UK route for a dog, but I brought one of my babies from the DR to Florida without any problem. Certificate from any Vet showing All Shots ($1,000 pesos) are current and and an air carrier approved travel kennel (mine was the largest kennel for my 90 lb puppy). Cost on AA was $75 USD, reservations required. At airport (AILA) I needed to get Offical of Sanidad to give me another form which he filled out (Name, aminal species, breed, etc.) another 300 pesos (just another tax). Arrived Miami, straight through and out. My puppy is really happy at her new home.