Is it permissible to donate as charity the amount of money equivalent to a pair of socks that my young daughter took by mistake, given that it's impossible to return them to the shop owner after more than twenty days?

After repenting to Allah for the delay, the socks or their price must be returned to the store, even if indirectly. Donating the price is not sufficient as long as the rightful owner is known, in accordance with the Almighty's saying: {Indeed, Allah commands you to render trusts to whom they are due}.