In the click event of symbol_1 -> button write this:
var stage = sym.getParentSymbol();
var sym2 = stage.getSymbol("symbol_2");
sym2.$("Text").html("NewText");
This code works if both symbol_1 and symbol_2 are children of Stage. Please note that symbol_1 and symbol_2 are the instances names of the symbols, as they appear in the "Elements" panel (not in the symbol library)