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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Throwing the pebbles on the first and second day on behalf of your parents and wife is acceptable, Inshaa' Allaah. Appointing someone to throw the pebbles on one's behalf is acceptable provided that one is unable to do that himself due to sickness, being of an old age or severe hardship because of crowdedness and the like. As regards the issue of throwing all the pebbles at once on the third day, which did not fall in the basin, and you only threw the smaller pebbles, then all of this is not permissible. Ibn Qudaamah said in Al-Mughni: 'The pebbles should fall in the basin, if they fall outside the basin then according to all the scholars this is not sufficient.' He also said: 'If one throws the pebbles at once, then that is not correct and one should throw them one by one, this is the view of Imaam Ahmad, Ash-Shaafi'ee and Maalik.' However, the scholars differed with regard to neglecting the throwing of one pebble or more. In our view, a sacrifice has to be offered by each one of you because of not throwing the pebbles on the third day. So one sheep has to be slaughtered on behalf of each one of you in Makkah, and it should be distributed to the poor there. But you are not required to do anything regarding the delay of offering the sacrifice. You could appoint someone in Makkah to do this for you as you have already left it.
Allaah knows best.