My ex and I have established a 50/50 child sharing without the courts. We were never married. She is now dating someor with violent felony convictions

The only way to have any legal input in this situation is to have a legal establishment of paternity with a time-sharing plan that is approved by the Court.  At this time you do not have an enforceable time-sharing plan, although it has been working thus far.  As for the new person with the violent felony convictions, she can date whoever she wants and the Court will not prohibit her from dating this person.  The focus is whether this person is around your child and if there is any violence between your ex and this person.  If there is violence then you would want to file an action to establish paternity and time-sharing for which you can work to have your child out of that situation.