Does one's Wudu become invalid upon feeling the discharge of secretions—of which the questioner was not certain—that had been discharged due to annoyance and anger with children?

Discharges invalidate ablution because they exit from one of the two private parts, requiring a re-performance of ablution and prayer. This is if you are certain of their exit. However, if you are in doubt, the doubt is not taken into consideration. You should try to treat the intrusive thoughts by supplicating and humbling yourself to Allah, and by seeking medical treatment.