Is the agreement reached between the husband and his ex-wife's family to waive part of the gold and the deferred dower in exchange for her obtaining a swift divorce permissible in Islamic law, knowing that the husband intended to divorce?

If the agreement was made with your permission, it is valid. If it was not made with your permission, then its validity depends on your approval. There is no injustice to your wife in this, but if you wish to give her what was stipulated in the first agreement as an act of kindness, you may do so.