I think getting rid of her simplifies a very complex problem and I understand that since you have a child together, it behooves you to try to stop this inappropriate and hurtful behaviour of hers. I do agree, both that she sounds incredibly insecure (if you are good looking etc and this began from the time you moved in together) as well as that it may be symptomatic of deeper issues.

Is there a way you could try couples counseling with an eye to helping her discover a possible need for therapy on her own? If she refuses, then you may have to consider moving on...and of course, how to work this with your child because at the end of the day....your child is the most important person in this relationship.

Be well