All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Your case, dear questioner, is one of two:
You are either suffering from an illness allowing you not to fast in Ramadan or you are not. If you are suffering from an illness allowing you not to fast during the daytime of Ramadan, you are blameless for your intention for abandoning fasting, taking medicine or having sexual intercourse with your wife, if she is not fasting due to a Sharee‘ah-approved justification. In such a case, you are not required to fast and you are not like those who are not permitted to eat, drink or have sexual intercourse during the daytime of Ramadan. Still you are required to only make up for the missed days. Allaah The Almighty Says (what means): {And whoever is ill or on a journey - then an equal number of other days.} [Quran 2: 185]
However, if you are healthy or suffering from a minor ailment which does not allow you to break the fast, you are not permitted to intend to break the fast during the daytime of Ramadan. Moreover, you are not permitted to take medicine, eat, drink or have sexual intercourse. If you had sexual intercourse on the day when your fasting was invalid due to making the intention not to fast and taking medicine, the grave Kaffaarah (expiation) is due in such a case, since you violated the sanctity of time by having sexual intercourse. The grave Kaffaarah is freeing a slave; if you cannot do that then it is fasting two consecutive lunar months; if you cannot do that then it is feeding sixty needy people. The sequence mentioned must be observed, according to the majority of scholars.
Deciding to travel on that day does not allow you to make the intention to abandon fasting, use medicine which invalidates fasting or have sexual intercourse with your wife. Moreover, your travel on that day does not absolve you of liability and you are required to offer the Kaffaarah which has become due on you even before traveling. Likewise, the Kaffaarah is due on your wife, according to some scholars, unless she was forced to have sexual intercourse or had a Sharee‘ah-approved excuse to abandon fasting such as pregnancy or nursing. You and your wife are required to make up for that day.
Allaah Knows best.