First, I would suggest that you have him neutered, but either way I'm
sure we can fix the problem. You will have to implement some
leadership exercises into your daily routine (ie: sit, sit-stay, down,
down-stay, wait, and come). I come out one day and demonstrate the
techniques if you want. Next, make sure all of the affected areas have
been cleaned with an odor neutralizer and be sure to not punish any
accidents. I've discussed the use of a crate with you and I know you
do not want to crate him, so I would have to suggest the use of a dog
exercise pen for him to stay in (temporarily) while no-one is home.
You will want to start with the exercise pen only allowing him minimal
room. After one week of him staying in the pen accident free,
gradually increase the amount of space in the pen every 3 to 5
accident free days. If he were to wet during this time, lessen the
area of the pen. Continue in this same manner until he has earned more
freedom. (Most of the time he is in the house with you, he should be
asked to perform some form of obedience .)
Also, there should be lots of down-stay work in any area he has marked
and he should eat his meals in those same areas.
If he seems to have a "favorite" area to mark, you could spray a dog
repellant on those areas.
Last, but most importantly, make sure he gets lots of exercise every
day (this always, always helps with obedience problems). Let me know
how it goes. Happy training!!