Get specific names. The point of much commentary is that the test was to go against his nature and be willing just as Yitzchak (especially if he was 37) had to be willing to be sacrificed. However, Yitzchak's characteristic was strength and it was not as much of a test because once he died it would be over. Avraham would have to live with it and it violated the trait of kindness which was his essence. Part of the test was also to be willing and able to hear the angel and stop, which showed he was in control throughout.
I do not know about Kabbala but this is what the meforshim that I have read seem to say.
See for example what Rav Shimshon Refael Hirsch writes throughout the incident.
The meforshim seem to say that his is why it was the ultimate test of Avraham. The test of rejecting Yishmael was also a matter of his overcoming his natural compassion for his child. Indeed from the descriptions of the meforshim, the "sending away" was supposed to be a formal matter and should not have resulted in the danger to Yishmael's life. That would not have happened had Hagar not panicked and gotten herself lost. Avraham had contact with Yishmael afterwards and the meforshim state that Yishmael was one of the two attendants who accompanied them to the Akeidah site.
Rabbi Dressler speaks of the nekudas habechirah (the point of choice). A person faced with a trial in which the wrong answer goes against his natural tendency would not be "tested". For example, a person who has adhered to the strictest standards of kashrus throughout his life would not be tempted by a sale at Ruth's Chris Steak House (according to the ads it is among the top nonkosher dining places). However, someone who is just starting to learn about keeping kosher might find it a major trial. Some of the trials (such as Sodom) may have been tests as to how far his compassion would go. Or it may have also involved testing would he be in control of himself enough to stop praying.