The early stages of strict control can last days or weeks or months. The animals involved will set the pace. A first step in easing your supervision of the proceedings could be to remove the leash. Or you could leave the leash on but release Fido from the down-stay. Thumper can get used to Fido in a new position.
Training is communication.
It is a way of showing the dog that the noises that come out of your mouth have some meaning for the dog. A dog who has received gentle, positive, effective obedience training knows to look to his human for guidance when he's in a new or unfamiliar situation. A dog who goes bonkers and completely ignores you whenever the slightest distraction presents itself is not a good candidate for rabbit-friend. Training should build the bond of trust and respect between you and Fido. It depends on the dog.