La mano o sus manos

[heze74]

I am having an argument with my Venezuelan wife that I hope you can resolve. I was taught in high school Spanish class that when referring to hands, they are considered a unit. For instance, in the sentence 'Todos los niños deben lavarse ... después de comer,' 'la mano' is used rather than 'sus manos.' She insists that I am ridiculous to say 'Todos los niños deben lavarse la mano después de comer.' I understand what may be said on the street, but in official Spanish, who is correct? Would it vary from country to country?

Thanks for your help,
Eric