What is a Minyan to do if the Chazan accidently recited Kaddish after Shemoneh Esrei on a day that Tachanun is recited?
In the event that the Chazan began to recite Kaddish immediately after Shemoneh Esrei, instead of reciting Tachanun, some Poskim rule that Tachanun is nevertheless to be recited after the Kaddish. Others however rule that Tachanun is to be omitted and one thus continues with Ashreiy, or Kerias Hatorah. If the Chazan has not yet completed the Kaddish, then if he has not yet reached the middle of the second stanza of the Kaddish he is to be stopped, and Tachanun is to be recited.
 Lehoros Nasan 6/7; Halichos Shlomo 11/2; Rivivos Efraim 1/98; Piskeiy Teshuvos 131/4
 The reason: As Kaddish is considered a small interval, and was not Halachicly meant to be said, and hence one cannot compare this case to the case of exemption by an Avel.
 Directive of Chazon Ish, as brought in Orchos Rabbeinu 3/225
 The reason: As Tachanun is meant to be recited immediately after Shemoneh Esrei, and once it has been pushed off from its place, it is no longer said, as is the ruling by the house of an Avel. [See Admur 131/5]
 See Birkeiy Yosef 282/11; Shaareiy Efraim 7/33; Igros Moshe 4/70-13