Complex sentence: In Greig's version, Lady Macbeth is known as Gruach and outlives her second husband Macbeth (she had had Macbeth kill her first husband) to continue to claim the Moray claim to the throne via herself and her son by her first marriage.
Split into simpler sentences: In Greig's version, Lady Macbeth is known as Gruach. Having outlived her second husband Macbeth, after she had MAcbeth kill her her first husband, Gruach continued to enforce the Moray claim to the throne via herself and her son by her first marriage.