I think Barb did a pretty lousy job parenting Jenelle because, as was said up thread, she was way out of her depth. When Jenelle acted out Barb resorted to yelling and insulting her. And when that didn't work Barb didn't reassess or get help, she just doubled down on her anger and yelling. Even if she was right that Jenelle was a beast (and she was), Barb's actions did little to change her behavior.
That said I think she is absolutely right to maintain custody of Jace. Another abusive partner is reason enough but Jenelle's actions clearly show she hasn't stopped making poor decisions. And everything above applies to Jenelle. If she wants to change Barb's behavior she needs to stop whining/lashing out and do something. In addition to having legal channels she could also show that Jace is a priority by cooperating with Barb in parenting him. Maintain a regular schedule, see him as often as possible, and pay child support.