It's ambiguous. In the right context, you would be understood, but it's not as clear. "It is time to sleep for my children" sounds like you intend to sleep for the benefit of your children. The verb "to sleep" is hard to make ambiguous in this context. Anotger example may help highlight the difference:
it is time for you to die.
it is time to die for you.
The first is a threat; the second is a statement of self-sacrifice. When the prepositional phrase comes after the infinitive, it tends to modify it.
With proper context and emphasis you would be understood, but it's much clearer to use the prepositional phrase to answer the question "time for whom?" rather than "to sleep for whom?"
Sometimes there are several ways in a language to convey the same concept. But when translating, one should try to say it in the same way as it was said in the original language (where a matching construction exists).
It's my kids' sleeping time (note that the apostrophes are needed) would be grammatically correct in English. But it uses the genitive. The original sentence used the dative; it is possible to use the dative to say this in English too, so that is how the sentence should be translated.
It can be pronounced both ways. When it sounds like an actual "o" sometimes it appears stressed (on vocabularies and dictionaries for example), but usually... you just have to guess. It's something you learn by listening, with time. (This is what I understood from the various explanations.)
Katzner's Russian-English dictionary say парА is correct (but accusative is пОру).
It's obviously feminine, so, absent some sort of irregular ending, nominative singular парА is the only correct pronunciation. There are no other -a endings in the feminine declension table.