14 lbs is too long to fit under a seat in the cabin? I find that hard to believe. We have flown to Belize and Mexico with our 16 lb. Boston Terrier in a Sturdibag large travel kennel in the cabin of both USAirways and Delta with no issues whatsoever. Your two smaller dogs could go in one kennel together and the larger one by itself, and each of you have one kennel as your "personal item". Please check out the Large Sturdibag (
http://sturdiproducts.com/products/large-sturdibag-pet-carrier) and see what you think. You may have to use a different airline from your preferred one, but I am almost positive you'll be able to get them into the cabin of a plane.
And I totally understand -- our dog is our "baby" too, and we wouldn't even consider leaving her behind when we travel for an extended time.
Feel free to PM me for more information if you have other questions.