This is a bit too vague to provide an adequate answer to, but I assume there are court orders in place, so I'm going to say that while you can invite the child to your home, the child's agreement to the invitation is immaterial, meaning it doesn't matter if the child says yes or no - the child's care arrangements are governed by a court order and so cannot be amended by the child. Any amendment to the orders would be at the father's discretion since he has sole parental responsibility.