Is it permissible for the wife to demand the dowry amount agreed upon in the contract ($20,000) if she had waived or forfeited it according to the custom of her country, and received gold, money, and clothes of a lesser value?

If the prevailing custom in your country is that the recorded dowry (mahr) is merely a formality and not meant to be claimed, then your wife is not entitled to claim it. She is only entitled to what you actually agreed upon, for "what is customary is like what is stipulated." However, if this custom is not widespread, then you are obligated to pay the amount recorded as mahr.

If the wife mistreats her husband and harms him, or becomes disobedient (nashiz), then he is permitted to restrict her so that she may ransom herself with her wealth or waive her mahr, based on Allah’s Almighty قول (saying): (And do not make difficulties for them in order to take [back] part of what you gave them, unless they commit a clear immorality).