Does anything of my divorced wife's gold become obligatory for me after the court ruled that her right to it was forfeited in exchange for her taking items from the house, and I had lost many times the value of the gold in court?

Your ex-wife erred by going to court and claiming against you what she was not entitled to. The judge's ruling does not make lawful what is unlawful, as the Prophet, peace and blessings be upon him, said: "Indeed, I am only a human being, and you bring your disputes to me. Perhaps some of you may be more eloquent in presenting their argument than others, and I may rule in their favor based on what I hear. So, whoever I rule in their favor regarding something that rightfully belongs to their brother, let them not take it, for I am only cutting off for them a piece of the Fire."

If you lost double her dowry in the courts due to her false claim, and the judgment was issued in your favor, and your liability was cleared, then you have the right to demand from her what you incurred in court expenses. However, if she was truthful in her claim, then you bear the costs of her litigation, and you are then obligated to return two-thirds of the dowry.

Scholars have issued fatwas permitting the demand that a procrastinator or a liar bear the costs of a lawsuit. So, whoever incurs a loss due to a false claim or procrastination, the one responsible for that loss is the one who caused it.