Is it permissible to supplicate against a married woman who is having an affair with my traveling husband, and how can I supplicate to Allah for a response despite my shortcomings in prayer, and do I have the right to supplicate against the oppressor?

The woman who is having a relationship with the questioner's husband is disobedient to God, and supplicating against her falls under the category of supplicating against people who commit sins, which is a matter of disagreement among scholars. The questioner should advise her husband and explain the seriousness of his action, and if possible, she should advise that woman as well, while striving to supplicate for their guidance.