Kawasaki disease (KD) is a self-limited illness that affects the heart blood vessels (coronary arteries) of infants and children and is now the most common cause of acquired heart disease in children. A mixture of proteins from human blood (Intravenous immunoglobulin, IVIG) is a treatment that reduces the rate of the major complication of the disease: a bulging of the wall of the coronary arteries called an aneurysm. However, 10-20% of children are resistant to this treatment and the fever returns. These children have the highest rates of aneurysm formation and thus should be treated aggressively. Unfortunately, there are no guidelines for the best secondary treatment for these resistant patients because the problem has never been adequately studied. Most physicians choose either a second infusion of IVIG or an engineered antibody called infliximab that inactivates a molecule that promotes inflammation. This trial will randomize (assign by chance like the flip of a coin) IVIG-resistant patients to receive either a second IVIG infusion or infliximab and the response to treatment will be compared to learn which treatment stops the fever the fastest. In addition, parents and caregivers will provide observations about their child's response to the different treatments.