How sound is throwing the pebbles at the Jamarat before their aforestated time due to overcrowding and fear for children, and is it permissible for a wife to authorize her husband to throw the pebbles on her behalf for the same reason?

Stoning before zawal (meridian) is not sufficient according to the majority of scholars. Whoever does so and does not rectify it after zawal must offer a sacrifice (dam) to be slaughtered in Mecca and distributed among the poor of the Haram, or fast for ten days if unable. As for your wife authorizing you to stone on her behalf: if it is due to an excuse such as childcare or fear of harm, it is permissible. Otherwise, your stoning on her behalf is not sufficient, and she must offer a sacrifice (dam) or fast for ten days. For abandoning all stoning, only one sacrifice (dam) is required.