Nah theres something going on... What it is.... I couldn't tell you... but its unusual behaviour for a four year old to just suddenly start with.
Tbh because it's involving family members, I would look to the home.
Tia had a lot of issues concerning her father. And she would take these out directly on DH and me. She would act out in a way so as to push us away to see if we stayed and would come back. Also when we went away on our honeymoon she wet herself at night and she was 7 then... It turned out that she was worried that DH and I would go away now that we were married, never come back, start a new family without her and she would have to spend the rest of her life with Grandma.
Obviously that was NEVER going to happen, but little kids especially between 4 and 10 aren't able to differentiate between reality and their worries. We all worry ourselves silly over things, believing something will happen even if it's irrational... well little ones are the same, only they can't express this fear as we can, verbally, so it comes out as acting up, wetting themselves, doing odd things.
I doubt its school but it could be as its a big change in his life. He could have heard a kid at school talk about his natural father and that hes a bad dad etc... so you're OH's little boy has got it in his head that all natural dad's are bad... Although I would look to his mother as well.. has she got a new boyfriend recently, has his routine changed, has she got a new job... ? All things that would disrupt his home life and cause him concern.