The first appropriate adjective that comes to mind is carefree. It very much implies an environment in which the usual cares and worries of life are significantly reduced in importance.
If you want a noun, the entire period of time might be referred to as a getaway. This word has various meanings, but the connotations here clearly refer to the fact that the two people are escaping their usual troubles and daily routines, hence "getting away".
Slightly less apt adjectives to describe such a time (almost synonyms to carefree) might be untroubled, blithe, or laid-back. These adjectives could be applied to either the time the persons spent together or the persons themselves, really. Other words like buoyant or light-hearted however, apply better to the moods of the persons themselves.
Finally, if you are looking for verbs of the form "They were [verb] by worries.", you could use:
These are all examples of attributive verbs.