Should I report an instance of nepotism - misconduct in favour of sexual partner?
This could go very wrong for you. If you go around and tell people what you told us here this could be considered as defamation of the professor and I wouldn't be surprised if he outright sues you.
The questions you should ask yourself:

Can you prove that they indeed had a sexual relationship?
Are the other students of the professor indeed more skilled than the student he promoted?
If yes, can you prove this in any legal sense or is this just your personal opinion?

Especially if you think you are one of those more skilled students I would be very careful, this can backfire horribly. Bad performance in her PhD certainly is not enough to prove 2. There are a lot of people who don't perform well in their PhD and didn't sleep with their advisor. And even if the professor and the student are a couple now, this is in no way proof that they slept with one another during the time the professor advised the student and less so proof that he promoted her for sexual and not academic reasons.
Academia is always very concerned with integrity. Is it ethical to sleep with his students and betray ones wife? Of course not. But you shouldn't just think about some academic code of conduct the professor may or may not have broken, but about the very real legal implications you may face. You are risking a lawsuit in pursuing this further and your personal gain is absolutely zero.
If this would be taking place in Germany, then relevant for the discussion is the following paragraph:

Section 186 Malicious gossip (üble Nachrede)
Whoever asserts or disseminates a fact about another person which is
suitable for degrading that person or negatively affecting public
opinion about that person, unless this fact can be proved to be true,
incurs a penalty of imprisonment for a term not exceeding one year or
a fine and, if the offence was committed publicly or by disseminating
material (section 11 (3)), a penalty of imprisonment for a term not
exceeding two years or a fine.

If you insist to pursue this issue, I would strongly advise you not to mention the affair. Go to the board and tell them you think there may be a conflict of interest in the award of scholarship XY. Don't accuse the student and the professor of having had an affair, you can't say this for certain. As Buffy points out it is highly likely that the board already knows about the issue anyways - Leave it up to them to make the conclusions.