He said that if his wife gave birth to a third daughter he would divorce her, but he did not intend to divorce her

Praise be to Allah.

Your saying “If my wife gives birth to a third daughter, I will divorce her” 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, “If my wife gives birth to a third daughter then she is divorced,” 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.