The current dynamite recipe requires to build 3 standard TNTs first, and therefore requires a total of 15 gunpowder before you can craft dynamite. Unless you farm Creepers a lot, you usually have superior tools available before you have gathered 15 gunpowder. I therefore suggest to change the recipe to require 1 gunpowder, 1 sand and 1 string for 2 dynamite (15 gunpowder = 3 TNT = 4 industrial TNT = 32 dynamite, so 1 gunpowder ~= 2 dynamite).
This would allow players to use dynamite much earlier in the game, as you just need sand and wool (frequently available) and 1 gunpowder to craft TNT. This would be a more appropriate form of mining instead of using stone pickaxes.