Well what they did was impulsive from our point of view but thats cause we have know whats going on completely while they only know parts. Besides, can you blame them, Sokka finally had a chance to see his dad after what was over three years, so of course he would be anxous to leave and of course Katara would let him. Though I do admit that its kinda strange that Sokka didn't want to give Suki a quick hello before going but maybe he was just too excited about seeing daddy.
As for Toph, well it's kinda "Avata state" all over again. She was so desperate for her parents to accept her as the mighty bender that she is that when she finds even the smallest hope that she would finally get her parents acceptance,??she goes against her better judgement.
Besides, they had "defeated" Long Feng and ended the conspiriacy so were more or less feeling kinda??bullet proof (or fire proof as the case may be).