Is my repentance valid after slandering the reputation of the person who slandered mine, in an act of revenge against her? And is my action the cause of the difficulty in my provision? And what is the way to atone for this sin?

The default rule is the prohibition of exposing a Muslim and defaming them. However, the Sharia permits the aggrieved party to retaliate in kind, without exceeding the bounds, as Allah states: ﴿So whoever commits aggression against you, aggress against him in like measure as he aggressed against you.﴾

Ibn Taymiyyah said: "The wronged person has a choice between seeking retribution or forgiveness, and forgiveness is better. If he was wronged by being beaten or slapped, he may beat or slap in return as was done to him. If he was insulted, he may insult back in the same way, unless it involves aggression against a right of Allah or against someone other than the oppressor, such as cursing his father or fabricating lies against him."

The sin of verbal abuse falls upon the one who initiated it, unless the wronged person exceeds the limits of seeking retribution. Seeking retribution is permissible, as Allah says: ﴿And whoever avenges himself after he has been wronged – those have no cause for blame.﴾ and ﴿And those who, when tyranny strikes them, they defend themselves.﴾ However, patience and forgiveness are better.

Whoever has exceeded the limit in responding to ill-treatment must repent and seek forgiveness. If their transgression was without the other party's knowledge, it is better not to inform them, and to supplicate for them extensively, and praise them in the places where you defamed them. It is also essential to increase good deeds, as they erase evil deeds, and forgiving people is a reason for Allah's forgiveness.

Sins can complicate matters and deprive one of sustenance, and difficulty in obtaining sustenance may be an indication of a sin.

Signs of a sound repentance: that a person is better after repentance than before it, that fear of Allah's deception accompanies them, that their heart is wrenched with remorse and fear, and a unique brokenness that affects the heart, not felt by anyone but the sinner, indicating their submission and humility to Allah.