'If' he is as bad as you say?
It doesn't sound as if any of the long list of crimes he's been CONVICTED of including violence against the OP are a matter of anyone's 'opinion' - just fact! And as for not suggesting the father is a risk to the child - I think 'threatened that if he got to see her I'd never see her again' is pretty clear!
Fine, the OP could be lying about them but if that's the case the whole thread is null and void really and there's no point in posting anything!
OP as josie says, sounds like your MIL may not have a criminal conviction but there are a list of things you can cite as reason for there not to be any kind of face to face contact for a long time.
She has threatened you. She has colluded with your ex in lying to you about his location. Crucially, she has refused indirect contact and sent no cards etc. She has shown that she is hostile to you rather than supportive of you, which given the actions of her son against not only you but her granddaughter is astonishing. I think you have a strong case for arguing that not only would contact with her be damaging because of her continued support of your ex, the fact that she does NOT want indirect contact demonstrates that her motive is not to keep contact with her grandchild but to act for your ex in continuing to harrass you. Make it very clear that you offered indirect contact even though the man living with her was threatening your life and to abduct your child! This should demonstrate that you are not implacably hostile but seeking to protect your dd.
The point to return to forcefully is, she does not have her granddaughter's best interests at heart. She is trying to bully and threaten her mother into having a violent, controlling man come closer to her.
You offered indirect contact. If this was a different kind of grandmother, it sounds as if you would be only too happy to take the support offered in keeping contact with the family whilst keeping your daughter safe from her violent father. Maybe point this out.