Some interpreters of the Revelation suggest that Jezebel was the wife of the vision caster in Thyratira. Even though there are a few linguistic reasons for such an interpretation, I find none of them convincing in the least. Primarily (as I've written elsewhere), the angels to whom these letters are written are not pastors, prophets, vision casters, or even humans--they are angels as is consistent with the use of the term throughout the Apocalypse. Pastors and bishops are never called angels (or messengers) in the NT, and it would be a novel application of the term to use it as such in these messages to the seven churches.
Furthermore, since the same Koine word means "wife" and "woman", it is not necessary to interpret the reference to Jezebel ("that woman") as "your wife", even if an extra pronoun (your, second person, singular) is attested in some minority manuscripts. She is female, she may be married, but there is no way she is married to an angel! The bottom line: there is nothing compelling about such an interpretation, and much that militates against it.
Christ gives this self-styled prophetess time to repent of teaching and misleading Christians in Thyatira to commit sexual immorality and participate in idolatry. Of course, in that time she actually has an opportunity to lead more astray, although time granted for the one leading others astray is also time granted for those being led astray to come to their senses and repent. If they don't, they'll go down with her because followers never shed their responsibility for following what they follow. The Antichrist may be thrown into the fire first, but those who follow him get thrown in just the same afterward.
Striking her children dead is a shocking threat, not really unique in biblical revelation, but appalling to our modern sensibilities all the same. Whatever else that says about God, it certainly undermines any notion that he is the touchy-feely type that loves everyone unconditionally. God is love, but he does with people as he sees fit, and who is there that can argue with him about it or question his judgment? History has an ample record of bracing catastrophe, e.g. the Black Death (~1340's), the Shaanxi Earthquake (1556), the Spanish Flu (1918), the Boxing Day Tsunami (2004), and the Haitian Earthquake (2010), which should convince any of us that it is a fearful thing to be in the hand of a God who can suddenly bring us into judgment.
If one sees the name Jezebel as a merely figurative assignation, (i.e. there was not a woman actually named Jezebel in Thyatira), then I would think it was permissible to see her children along the same figurative line. In that case, the children would be her second layer or level of followers rather than actual biological offspring. Those she commits adultery with would be the first layer, those that are won to her way as a result of the first layer would be the children. All three (her, her first followers, and the followers of followers) are justifiably threatened with judgment, for none are innocent.
When God strikes in judgment, it is meant to get our attention, but does he do so just because he desires to demonstrate his wrath? I think that the answer to that question must be both yes and no. No, in that he didn't desire it within himself as if wrath were an attribute of his nature; yes, in that given rebellion, he does desire to respond to it with wrath. Apart from creatures rebelling, there would be no need for, nor any expression of wrath--God is not innately wrathful. He doesn't have to, and hasn't fixed the game just so he has an opportunity to hurt someone and break things, but when it comes to unrepented of rebellion, God wants folk to know what reaction to expect from him.
So never read the wrong message into his patient forebearance--God searches the mind and heart, with absolute transparency. And what he knows in secret, he'll make known in judgment seen by all.