Can a woman to produce two identical eggs during separate events of meiosis?

Sure, it's possible. uming no meiotic recombination, the odds of this happening are 1/2^23, which is about 1 in ten million odds. However, during meiosis, paired chromosomes recombine randomly - usually each chromosome arm undergoes one recombination event during every meiotic event. This VASTLY reduces the chances of two identical eggs forming - I couldn't even calculate the odds. However, they're still non-zero :).