A.P.
I have no advice for you, but I can't help thinking that dogs urinate to mark their territory; primates fling feces and urine when they are scared or angry. Something could be really wrong with your step-son. I agree that he needs more counseling than what he has received.
It is not worth divorcing over, but you and your husband probably need couples counseling, too. You'll soon have three children under five, you work, you husband is never home, and your step-son pees in inappropriate spots, on upholstery, no less. Honey, something is going to have to give, soon. Have you noticed SS picks hard to clean locations? That is certainly a way to get negative attention.
As a first step, ask you husbad to talk to his supervisor, to see if he can have everyother Saturday off, when his son is visiting. I think that is the least he can do for you and his son.
I'd also suggest, that since the weather is warmer, that he has to stay outside wearing swim trunks so he can just pee on the ground (with maybe backyard camping as a bonus) but I can just imagine how that would be interpreted to his mother and the howls coming from her, since you don't give him food either. Expect a visit from Chidl Protective Services if you try that.