Ridgetop
Herd Master
Neither of those puppies look like they are even part Tibetan Mastiff. I doubt that they are. How did the owner of the dam know she was bred to a Tibetan Mastiff? TMs are a fairly rare breed, and most owners of TMs are not interested in cross breeding.Did you actually see the Tibetan Mastiff? This may be a case of who’ your daddy?
Telling you that they were going to take the second pup to a shelter is a dead giveaway that the owner knew these were not good LGD prospects, and probably knew that the dad was not a TM.I doubt they’d take them back as they talked us into the second one by saying they were bringing her to a shelter if we didn’t take her.
I agree with Farmerjan. Dogs that are established livestock or poultry killers are difficult to break of that habit. And since these dogs seem to be resistant to any sort of shock collar, training, fencing, confinement, etc. you will never be able to train them to be a good LGD. In addition, if you are having to keep them locked in a trailer or dog proof kennel to keep them on the property they are not protecting your livestock.If a dog is going through fencing like that, and is unresponsive to the shock collar you are using, it has already developed the predator instinct and stopping it from killing the chickens is 99% unlikely. From the sounds of them going to the extremes they are to get out of the trailer, it seems unlikely to me that you are going to break them of the roaming habit either.
Honestly either take them to a rescue with explicit information of them killing any/all poultry and waterfowl... and their tendency to roam and inability to keep them in fences... or put them down and start with an adult dog like @Margali suggested.
Here is your problem: You said that you have close friends who have Akbash dogs. I am assuming that these are not the persons from whom you got your dogs since you said "They are 5-month-old (I was told) Akbash Tibetan Mastiff cross." While the mom of the pups may have been an Akbash (and unless you saw her registration papers she may not have been purebred either) there is nothing to say for sure that the dad was a Tibetan Mastiff. Again. most owners of Tibetan Mastiffs don't just let them run loose to breed the dog next door. Next there are good Akbash LGDs and bad ones. Not all purebred dogs from an established LGD breed are good guardians. Depending on the breeder and bloodlines some LGD purebreds are very bad prospects.
You need to dispose of these two dogs, either by giving them up to the animal control as livestock killers or putting them down yourself. If they attack and kill a neighbor's livestock, you will be liable for the value of the livestock, fines, and other legal problems. Regardless of what your husband wants to do, these dogs need to go.
Then add up the money they have cost you in dead livestock, fencing, shock collars, their purchase price, and other expenses in trying to contain and train them. For what you have spent you probably could have found a trained LGD or at least a good puppy from a reputable breeder who came with recommendations.
Get rid of those two dogs before they cause you to be involved in a lawsuit.