Perhaps asking, "What is resentment or bitterness?" would be a better approach. To my mind they seem to be a few steps along the line from whatever sets the children off. The two parts of the verse seem to be - if you set them off, what you are going to get (in the long run) is them being de-spirited /despondent. A definition like L&N's sort of puts the end at the beginning.Colossians 3:21 wrote:Οἱ πατέρες, μὴ ἐρεθίζετε τὰ τέκνα ὑμῶν, ἵνα μὴ ἀθυμῶσιν.
To look at it from the aspect of back translation, perhaps, "to make someone bitter" might be better expressed by πικραίνειν. Of course that might be the implied meaning of the overal phrase, but I think that the stated meaning of the word ἐρεθίζειν is "set off", or "trigger". It seems that they have entered a possible contextual meaning in as a lexical meaning. Subjectively speaking, if there is any distinction to be made between bitterness and rebellion, then that could perhaps be put as alternate route - depending on how different people's emotions work.
How do others feel about L&N definition in this case?