My ex and I share joint legal custody. Does she have the right to dictate where and who the child is with during my parenting time?
No, she doesn't. She cannot control, regulate, or restrict who you see or what you do during your parenting time.
Generally, the only exception to this would be if there are provisions in your Parenting Plan or divorce decree that specify some sort of limitation(s) or condition(s). If there are none, then she has no authority to manage or direct what you do or who you see during your parenting time.