Is there a way to repel an undesirable or forbidden supplication, such as a person supplicating for physical harm or for not traveling, or mentioning something in their supplication that the one being supplicated against dislikes, and can this supplication be repelled by supplicating the opposite?

Nothing repels tribulation like supplication (Du'a), whether it is due to the supplication of another person or otherwise. So, supplicate to Allah with what you need, certain of a response, and ask Him to avert what you dislike and to grant what you love, for it is one of the greatest causes of good.

Supplication is a remedy; it wards off tribulation, prevents its descent, removes it, or alleviates it. It has three states with respect to tribulation: 1. It is stronger, so it repels it. 2. It is weaker, so it alleviates it, even if it is weak. 3. They are of equal strength, so each prevents the other.

It has been authentically reported from the Prophet, peace and blessings be upon him, that supplication benefits regarding what has descended and what has not descended, and that tribulation and supplication will contend until the Day of Judgment, and that supplication repels divine decree. If someone supplicates against you with something you dislike, repel the effect of their supplication with a supplication like it or greater than it. The effect of your supplication will be proportional to your sincerity and certainty of a response.