This is what we were taught in school here in Egypt, and it always seemed so cinematic.
Bonus questions if I may:
How involved was Ahmose's mother in getting him and his brother to lead Egyptians during the Hyksos reign? Our school textbooks always made it seem like she was the headstrong mother who pushed her children to free Egypt. Looking back it seems like a bit of fiction added for dramatic flair. Is it?
Did the Hyksos disperse after their defeat in Egypt? According to our books, Ahmose pursued them all the way as they fled Egypt, and then they were never heard from again. Again, is this conjecture or did Ahmose really drive the Hyksos out of existence?
Ahmose was of the royal house of Thebes and thus controlled Upper Egypt, he'd have no need to train a 'secret' army, he could do it openly.
I have never seen any art or reference to chariot horses being ridden into battle. It was quite enough for a pair of ponies, by modern standards, to pull a chariot with driver and warrior aboard at a gallop.
We know their height from skeletons found and chariots preserved. J. Spruytte reconstructed one, and found it much too small for his horses. He had to borrow a friend's ponies to test it (Ancient Harness Systems).
What the Hyksos became is one of those good archaeological mysteries. I have seen it suggested that their route may be the source of the Exodus story, making their later name "Hebrews." After all, they were the Shepherd Kings. This has a lot of problems, but there's a lot of handwaving about poor oral history traditions.