"Unethical" is an opinion and "immoral" is also an opinion. Therefore if it is your opinion that the relationship is "unethical" or "immoral", then either word is fine to use. If you are trying avoid expressing an opinion than "taboo" or "unusual" would be better because it is not a generally accepted, or common relationship.

See: https://en.wikipedia.org/wiki/Damage_(1992_film)

If you want to be neutral and careful in your opinion, you could say "unusual relationship". To be more critical, I would say "inappropriate relationship". I would never use "immoral relationship" myself as this this sort of terminology has "history". That is, it was/is used by some conservative or religious groups where they describe a relationship as "immoral" ONLY because it is *their* beliefs, not a more general belief. "unethical relationship" isn't very natural in conversation in my opinion. I would stick to inappropriate or improper if you want a meaning in the same general sense as this.

Yes. But alternate choices would be : An Immoral relationship. An Amoral relationship. An Improper relationship.

Unethical is a good term to use. It really depends on the context of the situation. Without further knowledge I can advise you that terms that describe that relationship are inappropriate, unethical, immoral, taboo. Also in other cases dishonest, wrong, and deceitful.