I care for him and I want to see him get help and set a positive example for our child.
Another way to approach this is to think about how you can be the positive example for your child.
I found myself focusing more on my child and less on my ex and that helped turn things around.
For example, your ex may be inconsistent in spending time with your child, which can be painful for a kid who expects both parents to provide stability and consistency.
If you help your child learn to reassure himself during struggles with difficult people, he will build a sense that he can tolerate difficult feelings. All the skills I learned here for dealing with someone with BPD were effective with my son many times over.
What is your child's relationship with your ex like?