Can my wife revoke my visitation if I own a pet and my child has allergies?

Only a judge can change your possession schedule. If the mother denies you access to your children under a court order, you can file for an enforcement. If your child is really allergic to the cat, you could take steps to keep the cat away from the child when you have possession. You may have to board the cat during that time or confine the cat to a certain room or let the cat stay with a friend when you have the children. If something gets filed in court, you don't want to appear that you put the cat before your child who is allergic to the cat.