What is the Shar'i (Islamic legal) stance on assisting a husband who is financially needy if he is educated and works in a simple profession, and is this considered "coddling" or not?

You erred by relaying the words your friend spoke about the other woman and her husband, as this led to estrangement between the two women. The correct action would have been to stop the backbiter from engaging in backbiting. The expiation for what you have done is repentance to Allah by ceasing the sin, regretting the action, resolving not to return to it, and seeking forgiveness from the wronged person. Since you have sought forgiveness from the woman through the aforementioned message, your repentance is, by Allah's will, accepted.