Is giving gold to one's husband to help him establish his company—with the intention of recovering it and later using it for the charity that the questioner intended for healing—considered a sin, especially since she was the one who offered it, despite her prior intention to give out the gold for the sake of Allah?

You are not required to give the gold in charity unless it is a vow (nadhr), and a vow is contracted by an explicit utterance or an implicit one coupled with intention. Your statement: "O Lord, I intend to give it out for Your Noble Face" is an implicit utterance. If you did not intend it as a vow, then you are not obliged to give it in charity, nor do you incur sin. However, if you did intend it as a vow, then you are obliged to give the gold in charity.

The fundamental principle is the obligation to give the vowed item itself. Some jurists, however, permit giving its monetary value. Therefore, if the gold was a vow, then according to the opinion that mandates giving the gold itself in charity, it is impermissible to lend it to your husband and then give its substitute in charity. If you do so, you are sinful. According to the opinion that considers its value sufficient, your sin relates to the obligation of promptly fulfilling the vow and whether or not you did so.