How to search opponents library when playing remote via webcam?
You need the proper tool. Webcams are not designed to keep track of MtG game states, so use a tool that can. There are many choices available MTG Online III (offical product, costs money for cards and packs), Apprentice (one of the first, but not a favorite of mine), Magic Workstation (my favorite), Magic Suitcase, Magic Studio, ...

The card manager keeps track of the game state, and the webcam allows you to observe the reactions of your opponent.