Does merely touching the hand of the fiancée's mother with lust—to the point of causing an erection—prohibit marriage to her daughter?

Your lustful gaze at your fiancée's mother does not prevent you from marrying her daughter, because what is forbidden is marrying the mother and consummating the marriage with her. However, you must fear Allah and not be lenient with forbidden glances, for it is a gateway to evil, and the reason for your feeling of lust is your mind's preoccupation with sex, influenced by corrupt media. A Muslim must elevate himself above constant thoughts of lust and know that this world is a place of work, not a dwelling. He must have high aspirations for Allah's pleasure and His Paradise. Marriage is recommended for those who can afford it, or fasting for those who cannot, along with supplication, diligence, striving against the self, getting rid of tempting influences, and filling the heart with the love of Allah and longing for Him.