How does Janette deal with her grief in "The Two Offers"?

After ten years apart, the cousins Janette and Laura have been reunited at the latter's deathbed. During that time, Janette has lived an independent life, pursuing a career as a writer. Laura, on the other hand, has been trapped in an unhappy marriage to an alcoholic gambling addict. The marriage is loveless, and it is notable that Laura's husband doesn't make an appearance at her bedside as she spends her final hours on earth in the bosom of her family.
Years earlier, Janette had advised her cousin to decline the two offers of marriage she'd received. But Laura was so anxious to avoid the fate of so many of her class and end up as an old maid, that she ignored Janette's advice and succumbed to the flattery of a handsome, but wholly unreliable suitor. In defying convention, Janette has been able to lead a happy, fulfilling, worthwhile life. Whereas Laura, by choosing to follow that very same convention, has had her life totally ruined as a consequence.
Despite their differences in class, and despite the divergent paths their lives have taken, Laura and Janette are still blood relatives. Janette is there at her cousin's death-bed right at the very end, grieving along with the rest of her family. Though deeply saddened by her cousin's passing, Janette is a strong woman and her strength of character is demonstrated by the way she handles her grief. As well as continuing with her writing career, she's determined to live her life according to a higher system of values than that which caused Laura so much misery. Laura's death has made Janette wiser; she realizes that life's too short to be frittered away on trivia and nonsense. She thus resolves to throw herself heart and soul into the anti-slavery cause. And her writing talent will be used in furtherance of her political ideas, not for fame or riches.
Janette openly admits that she's become what Laura wanted to avoid more than anything else: an old maid. But the difference is that she doesn't feel unfulfilled as a result; far from it. The reason for this is that she's lived her own life according to her own rules, realizing that true happiness lies in the regulation of our desires and the full development of our characters rather than in the fulfillment of our wishes.