Robert Baratheon literally tells ned in episode 1 or 2 exactly what Danerys will do when they stop for that picnic. Like, he foreshadows everything that will happen if she has a dragon. He didn't need a red witch or to look into the fire...he knew she needed to die ASAP.
I liked Ned at first but after some time and seeing how other characters in a similar position moved, I hate Ned. Man fukked up so many lay ups for honor.

where are you getting it from that Tywin wasn't taking Dany and her dragons seriously? Just because he wasn't boisterous about it didn't mean he wasn't taking it seriously. 

Full on Shadow government
you need to buy bricks before you build a house