Hello. I believe I can be of help to you with this issue.
Your post shows that you realize that the other kids are not being affected by the divorce but this particular child most definitely is. You describe a kid whose behavior suggests he is experiencing mild-moderate clinical depression. The boyfriend must stay out of the discipline, as he is doing. A major problem is: WHERE is this boy's primary male role model or father figure. Where is his dad? What is his relationship with his grandfather like? I ask this because when a child is depressed, they need an extra measure of ongoing regular attention, one on one, with an adult parent figure. In this case, someone needs to take this boy 'under his wing' and do things with him one on one---like a father would. You as his mother, need to take a few more minutes everyday to be with him, one on one as well. You have introduced a great deal of upheaval and insecurity into the lives of this kid---or maybe their father did
(I have no idea, of course).
I don't mean to be unkind or critical, but what is your boyfriend doing living with you and your parents? Is he going to school or? What is your future? Would he be in a position within say, 6 months to fully care for the family financially, 100%, if necessary (i.e., you'd move out, into a home of your own and be financially independent of your parents). IF NOT, if he isn't the quality of guy who can pull this off, I seriously question why you are diverting attention from your kids, your job/career, and the possibility of meeting someone who can 'step up' and fill this role. This last paragraph is really a side note to my primary response above. I don't know you at all of course and do not wish to be critical, but as an objective observer who doesn't know you, I do wish to challenge your thinking and judgment about this relationship. What do you think. Reassure me that the boyfriend is a solid, strong, capable provider, or very soon, will be and wants to be.