You need to go to court for more access. At the moment, you have only four nights a month and no full days. This does not allow your DH to parent.
Originally after his divorce my DH had an informal arrangement of 50:50 but this was then gradually restricted by his ex to a point where he was seeing his kids about 6 nights a month. Eventually his ex took us to court to further reduce access to 4 nights a month. We did a counter application and now access is back up to almost 50:50 and is court mandated.
We are still dealing with the legacy of 2 years of minimal contact. Though the relationship between my ex and his DCs remained excellent, inevitably the children's attitude to school and behaviour has been set by their mother's home and not ours.
I continue to be frustrated that my DH's passivity and desire to keep things amicable had such a negative impact on his children. As soon as access was restricted, he should have taken his ex to court. In this respect at least he failed as a parent.
Court was stressful and expensive but not as much as i had feared, and it has transformed our lives for the better. Not only do the SC see so much more of us, but there is less tension with his ex because the court has ordered the access arrangement. She can no longer unilaterally decide he is not allowed to see them. We are also seeing some gradual improvements in behaviour.
From experience, to impact his behaviour and values you need time with him. You can't change his mum, but your DH can step up as a parent. Sounds like both parents are equally failing him atm.