This moisturizing baby oil 2 break up the pump well. Organic and Allergy Free, Mama and Baby Safe Essential Oil Blends for all Ailments. Vaseline Intensive Care Cocoa Radiant Body Gel Oil, 6.8 oz. Johnson's Baby Oil, Body Oil. Many experts think the extra hormones a mother produces and passes to her child during childbirth cause the oil glands to act up.