So we know that Jon Arryn talked Robert out of murdering Dany and Viserys but why did Tywin never have them killed before Illryio took them and it would have been easy? We all know Tywin has no issue at all with murdering children, Robert would not have punished him for it, and they could be a threat to his grandchildren getting the Iron Throne.
It would not have been easy! You'll find me saying this a lot, but murders are not as simple to arrange as all that.
Tywin lives on the far side of Westeros. Dany and Viserys were in Essos, and for a period of that time, they were moving around. Even if Tywin had contacts in the Free Cities (we don't know either way) there's a huge amount of time lag. He can't be sure even what city his targets will be in. Which makes hiring an assassin very complicated indeed, let alone having an assassination carried out.
Like everyone else, Tywin just contented himself with the knowledge that two impoverished children stuck in Essos were unlikely ever to be able to muster the resources to threaten Tywin's grandchildren.