IMHO - this isn't about a steparents right - it's about yours. You have the right to your kids at XX time whatever day that is. How or who picks them up is your decision - not your Ex's.
IMO you tell - not ask - your Ex that your wife will be there at the assigned/agreed time to pick up the kids. She is to hand them over or face the concequences of denying court ordered visitation. She has no right to tell you who is allowed to pick the kids up unless they are a convicted child molester or something. Hand the kids over to your assigned person (which is well within your rights) or face court action. Period.