Try changing the soap you use on your toddler to a hypoallergenic, fragrance free version. You can also try applying lanolin (sold for nursing mothers) at bedtime.
Use a mild soap, such as Dove or Ivory, when you wash the child's hands, and apply a good thick moisturizer, such as petroleum jelly or Euciderm after every wash.
if its a simple condition of dry skin try Udder milk. Its thick enough to remain on the hands much longer than regular lotions or oils. its safe and not tempting enough to lick off
