House training abused JackRussel

Hi. 
I would suggest looking up crate training. 
As for the chemicals, if they don't want to buy something like nature's mircle or petzyme, I've heard vinegar and water in a spray bottle works, but I've not used it myself.
 

"Way to Go - How to Housetrain a Dog of Any Age" by Patricia McConnell.  It would make a nice little stocking stuffer for your friends. []

I'd recommend a crate, but he should be given plenty of time to get accustomed to it gradually and learn to like being in it and should never be left for long periods and should abolutely NEVER EVER be forced to soil in it.
 
Take him out to his toilet area at the times he is most likely to need to go - so, after eating or drinking, whenever he wakes up and after long periods of playing or chewing, also any time he looks like hes looking for somehwere to "go" or if he hasn't been out in a while.  When he "goes" give him a special treat he never gets any other time.  As he is going give him a cue that you can use in future to prompt him, but only say it once.  When hes done, walk up and give the treat - dont call him, make sure he knows this is for toilet not recall.  Be patient and vigilant and never punish him in any way for mistakes. 

If he is peeing very frequently and in small amounts, I'd also have the dog vetted to rule out a UTI. 

Hey!  Thanks for the replies!  I have suggested the crate, I don't know if they will use that idea or not since she is home all the time.  I also suggested that she have designated times to go out for that one thing, and also a designated area to go too so he knows what is expected when they go to that spot.
 
From what I understand he will pee out of excitement and/or fear, and this is the real problem.   If someone walks up to the door he will get excited/scared and just let it fly.  Is there anything you can do for that? 
 
He was terribly neglected and most likely abused.  When they rescued him he was staked outside far away from the house.  His collar had cut into his neck, and he was bloody around his neck.  had no water . . . you know the drill. 

ORIGINAL: acesmom

If he is peeing very frequently and in small amounts, I'd also have the dog vetted to rule out a UTI. 

 
I am positive they have had him vet checked, but I will mention that just in case they have not thought about it.