Complex sentence: William and his wife, James's elder daughter Mary, were recognised by the English and Scottish parliaments as king and queen, and as they had no children Mary's younger sister, Anne, was designated their heiress presumptive.
Split into simpler sentences: William and his wife, James's elder daughter Mary, were recognised by the English and Scottish parliaments as king and queen. As they had no children, Mary's younger sister, Anne, was designated their heiress presumptive.