Custody

My partner and I are ending things as a civil term where he can have our son at anytime he wants, only problem is I'm keeping my son away from his mother as she has caused myself and family nothing but distraught. She's rude and always cyber bullies me, I am 18 she is 50. She called me numerous of names and even said nasty things about my son, I didn't want to tolerate it so I deleted her off my social pages and phone contacts and deleted everything and continued to ignore her (She threatened myself and ex partner with court) but she didn't go through with it as she couldn't afford it. Me and my ex partner wanted nothing to do with her and her no where near our son, now we are seperatinf I am afraid she will slither back into my sons life without my permission. Please help what I can do. I am 100% to keeping my son away from her, he has my parent (Nana and Popop) my grandmother (nans) his fathers dad and girlfriend (Granddad and Grandma) all my sibling and fathers siblings (Aunt-Aunty/ Uncles) and many other family members around that are great and happy people. I want my son and myself to have nothing to do with her. She has been nothing but disgusting to me and my family.. Her daughter ran away at 14 years old with her kids and she hasn't done anything to get her back.. Her daughter would be 30 years now and the mother hasn't tried  find her or anything. She's threatened me if I had moved she will try to stop me.... I would love to move but want my son near his dad and my family. 
Any advice would be greatly appreciated as long as they are positive.