There are laws protecting childrens rights (look up the UNCRC) as well as parents rights, that may be a different angle you could try and maybe one you'd get legal support with. It's worth Googling fathers rights groups, there are a few out there and they may be able to offer you some support, or at least some good advice.
If that fails, assuming you haven't already, I'd suggest considering social services as the next point of call. I stopped DS's grandparents having access because of the "fine one minute, threats and world war 3 the next" issue (frustrating and exhausting, isn't it) and even though I'm a great parent, have a background in child psychology and DS is one of the happiest kids you'd meet, they still insisted on mediation to try and solve the problem and one social worker even threatened to put him on the child at risk register if I didn't participate because no matter how mental family members are, if the child has formed a bond with them it's considered in the best interests of the child to maintain that relationship.
As far as the accusations go, unless the ex can prove your husband is a danger to the child, she can't refuse access. Though, if you agree to supervised access, that may be a good starting point, as she may well believe there's some risk - people make up some nonsense to justify their actions when they're acting out of spite and often end up believing them.
When you went to court, was a Cafcass report done? What was the result?
As an aside, I would consider recording any future conversations with her. If she's claiming that her violent past as something she's moved past, you'll have evidence that's not the case and people with violent tempers and criminal convictions rarely end up with autonomy over a child once the relevant authorities are aware there is an issue of risk.
Oh, I almost forgot. If there's a court order in place granting visitation rights, it's a legal offence for her to refuse. If you have a court order in place at the moment, if she doesn't produce the child on the specified date at the specified time and in the specified place, call the police ;)