A lovely verb still widely used in Spanish, with the verb «soler»: In Spanish this sentence would be nearly identical: «La madre y el padre suelen dormir». Little reminders of how Romance languages, more than being just descended from Latin, are really just incredibly corrupted or simplified forms of Latin, if you squint hard enough.
Translation is also about what's more common or idiomatic in the target language. The verb "solere" is best translated as "to be accustomed to", and we can certainly say "Mother and father are accustomed to sleeping", but that has a different connotation than "Mother and father usually sleep".
As you say, "the more common use is accustomed to +_ing." But it is also possible to follow "accustomed to" by a noun, e.g. "They became accustomed to the darkness". In the case of "sleep", it can be either a verb or a noun, and I think that is what ARCANA-MVSA may be getting at. Without the "ing" ending there might be a tendency to interpret "sleep" as being a noun in the phrase "accustomed to sleep".
Exactly. In this case, the verb isn't just "accustomed"; it needs the preposition - "accustomed to." This means it's not immediately clear when what is being used is an infinitive form (since "to" is only mentioned once) versus when it is a noun.
"Accustomed to sleep" seems to me like the parents are used to sleep, just like they are accustomed to dreams and darkness. It's a noun.
"Accustomed to sleeping" seems to me like the parents are used to the action of sleeping - particularly in a certain way/at a certain time, since sleeping itself is not that unusual. ;) In this case, it's a verb.
Volgav vitsenanieff nivya kevach varatsach.