If someone purposely skipped Al Ha Nissim on Purim or Chankah do they have to repeat the Amdiah/Bircas Ha Mazon? I'm aware that if it was on accident they do not have to go back and repeat it.
The Biur Halacha to OC 114:7 quotes the Bach and Elyah Rabbah that the reason a Meizid (someone who skipped a part of the Amidah on purpose) returns to the beginning of the Amidah (or repats it) is because in this case, all Berachos of the Amidah are considered one.
If this is the case, we only return to the beginning of Amidah (or repeat it) in a case where one would be required to return to that Beracha if still in middle of a later Beracha. Since Al Hanisim would not require a return to the beginning of the Beracha if one noticed after that blessing had been completed (i.e. during the Beracha of Sim Shalom, as per SA OC 682:1), we can safely say that if an individual skipped Al Hanisim on purpose, he should not repeat the Amidah.
(There may be a reason to disagree with this logic of the Bach and Elyah Rabbah based on whether or not the opening Passuk of ה' שפתי תפתח is repeated, ואכמ"ל.)
I haven't done thorough enough research to see if there is a difference between Shogeg and Meizid in Birkas Hamazon as well. Either way, it is safe to assume that Birkas Hamazon should not be repeated, either because there is no difference between the two (and therefore will be treated as if it was skipped by mistake), or because it will have the same status as Amidah (and even in a later Beracha it would not be corrected, so we do not return for it).