I don’t think your husband can ‘rectify’ things said about him as such, all he can do is try to be a good dad and that will be what his son takes away from it all.
When I was a young child I saw my dad for two days every other week. By the time I was 10, I saw him for a weekend every 1-2 months. For the first few years there was ‘bad mouthing’ from both sides (mum and her family vs dad). I disliked all of it and all I took from it was that they wouldn’t stop going on about how much they didn’t like the other. As I got older, I started to tell them (all of them) that I didn’t want to hear it as it wasn’t my problem.
On the other hand, I knew that both of my parents loved me dearly and wanted the best for me. The issue was managing their relationship with each other, and thankfully they eventually learned to stop trying to bring me into that discussion and gradually even became amicable. I was never in any doubt that my dad wanted to be there for me, despite criticisms of him and not seeing him much, just as I was in no doubt that my mum did absolutely everything she could for me, despite claims that she was trying to ‘take me away’.
I felt confident of that because of how they treated me directly and what they did; my dad dropping little things off to the house that he saw and thought I’d like (not about money, things like a book I might like to read), helping me with homework, calling me very regularly just to chat and catch up, and my mum never actually blocking any contact, letting me spend holidays with dad and his parents, even attending events with my dad’s family even though she felt so uncomfortable because she did it for me, and being the parent who raised me day by day.
They probably made some mistakes along the way, and I didn’t always enjoy it, but regardless of what happened I always felt that they both loved me, that they were just a bit misguided and angry at times.
So the point of reflection from my experience here is, how is your husband’s relationship with his son? How does he try to be there as a dad, in whatever form, even if he only currently has access for 6 hours a fortnight?
FWIW I know someone else in a similar situation (some years ago), very acrimonious separation and the mum did not like the dad at all and would regularly speak very badly of him to the children. Children visited the dad every other week, then once a month as they got older and wanted to see friends. The dad was really worried about how their relationship would develop, did what he could in terms of supporting them financially and speaking with them as regularly as they would allow (phone calls and the like, in addition to their visits, trying to help with things like exams, university and so on). Both children are now adults and both have developed a positive relationship with their dad, even though at one point it looked in jeopardy, and both regularly catch up with their dad by phone and in person even though they don’t live in the same city (they actually come to visit him, as well as him going to visit them).