Anyone own a Jack Russell?

My boyfriend and I rescued this jack russell puppy from a friend. His female JR had a litter under the porch and the puppies ended up infested with fleas, ticks and worms. We got one, got him healthy, FINALLY, and we love him dearly. Here's my question: I know they are high strung dogs and we were prepared for that. I know he's only a puppy but GAWD DAMN he seems to be getting worse about not sleeping all night and messing in his cage. He is almost 4 months old and in the last two weeks, he whines/barks at around 1 or 2 a.m. to go out and then again at 3:45 a.m. Sometimes he whines causes I guess he wants out of his cage to be with us but we aren't sleeping anymore. I'm averaging about 4 good hrs. of uninterrupted sleep a night then about one hour after I finally get back to sleep. Are Jacks different in training them than other breeds? We let him run for about 1.5 hrs in the morning and about 3 or so hrs. at night for exercise and to "wear him out" so he'll sleep at night. Ain't workin'! I haven't trained a dog in over a decade and neither has my boyfriend although he has had many more than I have but even he is ready to ship the poor little guy off.
I'm trying to stay patient and remember he is just a puppy but he was doing so good until recently so I wonder what I'm doing wrong.


