The hadeeth “Whoever fasts will have one reward and whoever breaks his fast will have two rewards”
The well-known hadeeth concerning this is that which was narrated by Muslim in his Saheeh from Anas (may Allaah be pleased with him) who said: “We were with the Prophet (peace and blessings of Allaah be upon him) on a journey. Some of us were fasting and some were not. We stopped to rest on a hot day. Those of us who had the most shade were those who had cloaks, and some of us shielded ourselves from the sun with our hands. Those who were fasting could not move and those who were not fasting got up and set up tents and gave water to the riding animals. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘Those who are not fasting have gotten the reward today.’” (Narrated by al-Bukhaari, 3/224; Muslim, 1119). According to another version narrated by Muslim, he said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) was on a journey and some people were fasting and some were not. Those who were not fasting worked hard, but those who were fasting were too weak to do some kinds of work. He said concerning that, ‘Those who are not fasting have gotten the reward today.’”
The meaning of the two hadeeths is clear, which is that availing oneself of the concession allowing a person not to fast whilst travelling when it is difficult and is very hot is better than taking the more ambitious option which is fasting.
With regard to the hadeeth which you mentioned, I do not know of any source for it.
And Allaah is the Source of strength, May Allaah send blessings and peace upon our Prophet Muhammad and upon his family and companions.