Your saying âIf my wife gives birth to a third daughter, I will divorce herâ comes under the heading of promising to divorce in the future. If she gave birth to a daughter but you did not divorce her, then nothing has happened. This is confirmed by the fact that you did not mean what you said: you did not intend for a divorce to happen at that time and you did not make it conditional upon her giving birth to a daughter.
But if you said, âIf my wife gives birth to a third daughter then she is divorced,â then divorce takes place if she gives birth to a third girl.
You should beware of using the words of divorce (talaaq) in ways other than that for which they were prescribed, namely ending a marital relationship when the husband decides to do that for reasons which make it permissible to divorce.
And Allah knows best.