Why did he tell her to disguise herself?
Radak: He knew that Achiyah hated him because he departed from Hashem's ways. He thought that if Achiyah knows that it is his wife, he will give a bad Nevu'ah.
Why did he think that it will help if she disguises herself? Will the Navi not know via Ru'ach ha'Kodesh?
Malbim: (a) He did not want people to know that his wife asks from Navi Hashem, and say that he believes in Navi Hashem and not in Nevi'im of the golden calves. (b) When a Navi sees with Ru'ach ha'Kodesh, he attains only the matter he wanted to know, just like a question to the Urim v'Tumim. If he does not know that she is Yaravam's wife, he will ask only about if her son will live, or he will pray for him. If he knows that she is Yaravam's wife, he will prepare himself to know and influence all matters of Beis Yaravam, for it pertains to Klal Yisrael; perhaps he will give a bad Nevu'ah.
Why did he say "Asher Diber Alai l'Melech Al ha'Am ha'Zeh"?
Radak: His Nevu'ah is fulfilled - just like he said about me, so happened. What he will say about the youth is true.
Malbim: Just like my greatness came via his Nevu'ah, I can be demoted if he will give a bad prophecy about me, like happened with Shmuel and Sha'ul.