Is it permissible for a wife to return to her husband after three divorces, knowing that she returned before the completion of the waiting period (iddah) after the first and second divorces?

What you uttered the first time is considered a conditional divorce (talaq mu'allaq). If you intended divorce, it takes effect by agreement of the jurists. If you intended a threat, there is a difference of opinion regarding it; the majority view that it takes effect, while Ibn Taymiyyah holds that it does not. As for the last two times, the divorce has taken effect in both instances.

If the first divorce is effective, then your wife has become irrevocably divorced from you (baynunah kubra), and she is not lawful for you until she marries another husband, based on the Almighty's saying: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband. And if he [the other husband] divorces her, there is no blame upon them both if they return to each other and assume that they will maintain the limits of Allah." {Al-Baqarah:230}. If the first divorce is not effective, you are permitted to take your wife back with a new contract, due to the completion of her waiting period (iddah).

It is not permissible for a wife to leave her husband's house except for a legitimate religious excuse. A wife's request for divorce does not prevent it from taking effect if the husband pronounces it, and it is forbidden for her to request divorce without a legitimate religious reason.