A big no to the train. You'd have to change at Reading and likely somewhere else too, and it's hard to tell which train to take when you're not familiar with the system. Plus, with that amount of luggage (the pet carriers alone!) it'd be a nightmare. Are you sure there's not a cheaper taxi service? My MIL got us a taxi from Somerset to Heathrow and back for a lot less than $1500, and it's only an hour or so farther to Exeter. IMO that's the best option--straight to where you need to go, no hauling luggage, no driving in traffic, etc.