Will the wife be sinful if she agrees to a divorce by mutual consent, while she was against it and her husband insists upon it, and is it permissible for her to perform Istikhara concerning this matter?

If the wife's situation is that she refuses divorce, then she does not sin by agreeing to the husband's desire for divorce. The noble prophetic hadith: "Any woman who asks her husband for a divorce without any strong reason, the scent of Paradise will be forbidden to her" refers to one who seeks divorce without a legitimate Sharia-compliant justification. It is permissible to perform istikhara (prayer for guidance) regarding whether to proceed with a consensual divorce or not, because istikhara is for permissible matters. Dialogue between the spouses is recommended, and the mediation of good and wise people for reconciliation, along with seeking help through supplication.