Does a conditional divorce take effect if the wife spends money gifted to her by her husband on household necessities, knowing that the husband intended for her to keep her money, and that the couple agreed upon a stratagem to avoid the divorce taking place? And are their ignorance or interpretation taken into consideration so that the divorce does not occur? And does this fall under the excuses of the jurists, by analogy with forgetfulness?

Your interpretation is unacceptable. Take the saying of Sheikh Al-Islam Ibn Taymiyyah regarding conditional divorce (talaq mu'allaq), which obligates you to an expiation for an oath (kaffarat yamin) because you did not intend to effect a divorce, but rather to emphasize to your wife and prevent her from spending her money. Although this opinion differs from the majority view, it is permissible for someone afflicted by waswas (obsessive doubts) to adopt the easiest of opinions. We advise you to turn away from these waswas and seek help from Allah.