What is the common denominator between the happiness derived from family life and the happiness derived from being a recluse?
The common denominator is the feeling of pleasure. Apart from that, the conditions giving rise to the two types of pleasure are different. The conditions giving rise to the pleasure of the household life is craving & affection where as the conditions giving rise to the pleasure of the recluse life is the abandoning of craving & affection.
Monks, there are two kinds of pleasantness. What two? Household pleasantness and the pleasantness of one gone forth. Of these two, the pleasantness of one gone forth is better.
Psychologically, the answer is that both probably experience both happiness and dukkha. You do not specify whether or not they are practicing mindfulness meditation or learning Dharma. It is also possible for either one or both to already be Enlightened or to be Enlightened soon. Either one may be experiencing dukkha more than the other.
Buddha taught gradual training. There are many stages of happiness you can experience before you become a recluse. This is explained in Sutta such as many kinds of happiness.
Though some might say, 'That is the highest pleasure that beings experience,' I would not grant them that. Why is that? Because there is another pleasure, more extreme & refined than that.>