The tumors could have been
a transitional, basal cell, or even Mast cell cancer. It could have been locally invasive or metastatic. It should not have taken surgery 8X over to get an accurate pathology reading. For a tumor like growth to reoccur and grow so rapidly should have been clue enough for the Vets that a cancer was involved.
As for your other lab puppy you could have a combination of hip dysplasia and elbow dysplasia.
Another thing you should discuss with the other Vet and/or specialist is whether the thyroid problem is completely under control. Hypothyroidism can be associated with muscle weakness, and nerve damage which can lead to lameness. Although your dog is on thyroid medication, there may be periods of the day when it doesn't have enough thyroid hormone. If Xrays eliminate the dysplasia as a problem, look to the thyroid control as a possible cause. It may take several blood samples to measure the T4 throughout the day.
As for the question why you are having these problems- genetics. What does it really mean for the sire to be a 4X field champion? It means the dog excelled in the expected behavior for the breed in hunting. What does it mean per the health of the dog? Nothing! The breeder claimed the sire died peacefully of old age??? Euthanasia can be very peaceful. It's quite obvious the mother had a severe thyroid genetic defect she was passing onto her offspring. Chances are she was showing clinical signs herself, despite the breeder's claims.
Nothing beats a Lab for temperment. :)