The problem here is that when you say some children it is often interpreted as meaning children in general—not specific children. Also, without further clarification, it's not clear if you're actually talking about one or more broken families when it comes to a specific child.
To avoid any misinterpretation, you have to be very explicit.
(1) Talking about each single child in a group, who has been on their own:
Each child is from different multiple broken families.
Each child is from a different single broken family.
(2) Talking about all of the children in a small group, who have, together, been placed with families:
All the children are from the same multiple broken families.
All the children are from the same single broken family.
(3) If you don't care about being so specific, and it doesn't matter if some children in a group grew up with others or on their own, but you still want to indicate just one family or several families:
Some children are from multiple broken families.
Some children are from a single broken family.
(4) Finally, the most general statement, where it doesn't matter if children in a group were paired with others or not, or how many families they grew up in (or even if you're not talking about a specific group at all), then you can fall back to your general statements. And, with those, it doesn't matter which statement you use:
Some children are from broken families.
Some children are from a broken family.
Both of these last statements could be interpreted to mean anything.