The order, itself, didn't have to be specifically programmed into the clone troopers. They were bred to be compliant to the Republic, and Palps is the head of the Republic. He need only give the details to the clone commanders, which would be passed down to the troops, under the proviso that no details of the order be told to anyone. The clonetroopers have no choice but to comply.
"How come when the babies were born Vader and Sidious did not feel a huge disturbance in the force?"
Probably the same reason why none was apparently felt when Anakin was born. Otherwise, he would have been found a lot sooner.
Besides, Palps didn't sense Luke until he started using the Force in earnest. This, along with the fact that Vader sensed Luke (actually Obi-wan, I believe) in the trench, and Luke used it to destroy the DS were all pretty big hints in and of themselves.
"Didn't Vader/Palpatine sense anything? Vader knew he would have a child, he never bothered to look for it in Tatooine? Perhaps while visiting his stepbrother, Owen Lars...? Or visiting his mother's grave, right NEXT to it?"
Watch Padme's funeral procession. She is made to look like she is still pregnant. Force sensing is nowhere as distinct as you guys make it out to be.