RE: Is it possible to have a housepet hunting dog?
Since you don't seem to be referring to using the dog to actually hunt, just tag along on some varmint hunting, as long as you have a dog that listens there would be no reason to leave him home. Especially groundhogs. Switch to coyotes or other varmints you may want to be sure of your control over the dog.
If you are seeking companionship while hunting, you really should consider using that golden or lab to hunt birds.