Also - you WILL need to have some degree of dealings with the child's mother and you need to learn to have a civil, respectful relationship with her. You will not be allowed to bypass her entirely, nor should you try. While it would be nice if your wife and your ex could meet and become friendly, not everyone lives in happyland where the children's needs come first. They don't NEED to have any contact at all.
You're best off telling your wife that she can find somewhere else to stay while your child is (eventually) visiting. With the attitude she has now, it's clear she is not going to treat this child as a member of your family, so she's better off getting lost. If I were you, she'd be getting lost permanently, but then again I would never have married someone who had a problem with a child they knew I had before I'd even met her. Or whatever the exact situation is. You're going to have to jump through plenty of hoops to establish a relationship with this child, your own wife's insecurity should not be one of them.