What is the way to repentance and salvation from the consequences of a major sin I have committed, while facing the threat of its exposure and feeling a sense of despair that drives me to contemplate suicide, yet still retaining religious scruples?

The questioner's regret for what she did is the beginning of a sincere repentance, which does not require informing the husband of what happened, and supplication for him is sufficient. Her relative's threat should not be heeded; rather, he should be threatened with exposure of his incitement to divorce. Suicide is not a solution; rather, it is a greater misery. One must be careful not to be lenient in dealing with a non-mahram (definition); because being alone with him may lead to temptation. A Muslim may be tested in his faith, and that does not mean that Allah has forsaken him; rather, it may be a test of his sincerity.