All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Throwing pebbles before zawal is not sufficient to meet the obligation, according to the majority of the scholars; and that is the opinion which we opt for. So it is due on the one who threw pebbles before zawal and was unable to do it after it to sacrifice a sheep in Makkah and distribute its flesh on the poor of the Sanctuary. If he failed to do so, then ten fasts would be due on him. If you threw the pebbles before zawal by way of following the opinion of a scholar who is reliable in your sight, then we hope that nothing will be due on you, Allaah willing.
As for your wife deputizing you to throw pebbles on her behalf: if you both could not take care of the children unless she stayed with them, and if you feared for her in case she went alone to throw the pebbles and you took care of the children, then this would, seemingly, be a legal excuse that makes it permissible for her to deputize you to throw pebbles on her behalf. However, if she was able to throw pebbles by herself with no fear of harm on her, then she did wrong by deputizing you to throw pebbles on her behalf. In that case, your throwing pebbles on her behalf would not be sufficient for her to meet the obligation. So it is due on her to slaughter a sacrifice and distribute its flesh among the poor dwellers of the Sanctuary. If she failed to do so, then ten fasts would be due on her. Only one sacrifice is due in case of failure to throw all pebbles. According to Sharh Al-Muntaha:
If one delays it, i.e. throwing pebbles, till they, i.e. all days of Tashreeq, are over, then only one sacrifice will be due because the person has missed the time of throwing pebbles. (For skipping all days of throwing pebbles) the ransom is confirmedly due depending on the statement of Ibn ‘Abbas who said, "If one leaves or forgets a ritual, then a sacrifice will be due on him."
Allaah Knows best.