I assume thomas.ech meant 'children' as in '[unspecified/mixed gender] offspring', not just unrelated young people.
Is बेटे used for mixed gender group of offspring, or only by people / regions that would anyway call their daughter(s) बेटा ? Or is बच्चे used to mean both related and unrelated groups, as the English 'children' is?
बेटा is only ever used for daughters when directly addressing them. Terms of address are huge in Hindi and don't necessarily always correspond to their literal meaning.
When used otherwise, it unambiguously means 'son' and by extension बेटे means 'sons'.
बच्चे may be used for both related and unrelated groups. Eg: पार्क में कुछ बच्चे खेल रहे हैं ('Some children are playing in the park' - where it refers to random kids), कल मेरे बच्चे कनाडा से आ रहे हैं ('My children are coming from Canada tomorrow' - where it's referring to your offspring who may well be adults).
उसके* (Though here it would actually be उनके) Yes, you can however generally when you talk about people, उसके / उनके is used rather than उसके पास / उनके पास, the पास form is used more for things you literally own, like items. So familial relations, friends, relationships, when you say things like "My daughters/sons/wife/friend/mother/brothers/etc," it's better to use उसके / उनके.
उनके is plural 'they' while उसके is singular (he/she/they), based on my understanding. If 'they have' is meant to be plural, उसके would be incorrect (though English is wishy-washy on when they is singular or plural). So उसक दो बेटे हैं would be he/she/they (singular) has/have two sons, while उनके दो बेटे हैं is they (plural) have two sons.
At least, that's my understanding. I'm also learning, though!
You choose between उनके/उनकी/उनके based on the gender/number of the noun phrase that comes after it (ie, the thing being possessed) and not the gender/number of the possessor. Since बेटे is masculine plural, you have to stick to उनके no matter the gender of the parents.
'They have two daughters' would have been उनकी दो बेटियाँ हैं। even if the 'they' refers to 2 men.