Co-parenting with a bully will have many features in common as co-parenting with a narcissistic personality.
However, not all narcissists are bullies and not all bullies are narcissists.
To differentiate, the overt bully is straightforward with little subterfuge. This person will make demands upon you and use threats or intimidation to get you to give in to those demands. This kind of bully is usually less sophisticated than those with a narcissistic personality. This person is also distinguished from those with a high conflict personality in that they aren’t necessarily seeking to tie you in knots or undermine your parenting. It’s just that when they want something, they don’t ask. They demand and threaten to back up their demands. This is more akin to a form of domestic violence of the coercive controlling type.
This kind of bully can use anything at their disposal to intimidate you. They may threaten to release untoward information, they may stalk or harass, they may threaten physical harm or property damage.
To be clear though, the bully in these circumstances may be acting criminally. Although intimidating, these are situations when it is best to consult with a lawyer or at least talk with a counsellor at a shelter.
To end this kind of bullying, a restraining order may be helpful, but that would require you to make a formal complaint to either police or the Court. If you seek to make a complaint, having evidence to back up your claim of bullying, harassment or intimidation will be necessary so that the complaint doesn’t appear to be generated out of spite or anger.
These can be very frightening situations. Having access to a counsellor, such as at a shelter, or your own lawyer, may be required to sort out a plan for your moving forward safely.