To relieve your daughter's dry and irritated hands from frequent handwashing, you can try using a gentle, unscented soap like Dove. You can also opt for a cleanser containing ceramides such as CeraVe or Cutibase to help repair the skin. Make sure to rinse off any residue thoroughly and pat the hands dry gently. Additionally, applying a moisturizing cream, especially one with ceramides, after each handwashing can aid in skin repair. If the symptoms do not improve after a week or worsen, it may be necessary to consult a pediatrician for a more effective treatment. You can even consider having your daughter wear cotton gloves after applying the moisturizing cream before bedtime to help soothe her hands.