This happens to me a lot on Mondays and Thursdays: I'm just putting down my head to finish Tachanun when the baal tefilah says kaddish, the aron is opened and the Torah is taken out. Do I stop what I'm doing? Stand up? Answer "amen" and "y'he shmei rabba" to the kaddish? Say "vay'he binsora"? Or should I continue with Tachanun until I'm done?
Siach Tefila question 137 & 138 indicates as follows. If one is in the midst of the actual Tachanun (the part where you place your head on your arm) then he should finish the Tachanun, however if one is in any other part then he should stop and say Vayehi Bin'soa.