Does expiation become obligatory for one who broke their fast in Ramadan due to travel, then broke it on the following two days due to fornication? And when does the fasting of two consecutive months become nullified if expiation becomes obligatory?

If the journey is one that permits breaking the fast (a distance of 83 km or more, not for a sinful purpose, and without the intention to reside for four days or more), then no expiation is required for breaking the fast by intercourse. Repentance from adultery is obligatory.

However, if the journey is one that does not permit breaking the fast (such as a journey for a sinful purpose, or a distance less than the travel limit, or the intention to reside for four days or more), then fasting is obligatory, and expiation is required for intercourse (freeing a slave, if not found then fasting for two consecutive months, if unable then feeding sixty poor persons). The expiation remains a debt if you cannot find what to feed the poor persons with.