Is expiation obligatory for one who swore an oath to obey her husband in all that he asks of her, and then violated her oath by giving her son soda after her husband asked her not to let him drink it, and does this oath of hers remain valid for life?

The questioner's oath is binding upon her to obey her husband in not giving their son soda (cola). Breaking this oath occurs with any transgression, and she is liable for a single expiation for breaking an oath, and the oath is thereby dissolved. If her intention was to repeat the expiation every time she transgressed his commands, then the expiation multiplies with each transgression. There is no difference in the occurrence of breaking the oath whether the husband knows or not. The oath is dissolved by giving her son soda or any other transgression without the husband's permission, and a single expiation is required unless she intended to repeat it, in which case she is bound by what she intended.