Unless the reader is unusually precise, I'd say that both #1 and #2 would be taken to express the same as #3. However, this is ELL, so let's be unusually precise. Taking #2 first:
- There are many girls in the school from poor families.
I agree with Kate that as it stands, there is an ambiguity. It is possible to interpret #2 as referring to a school that was set up by some poor families where many of the students were (not necessarily poor) girls. Kate's proposed solution fixes that:
2'. There are many girls in the school who come from poor families.
But #1 also contains an ambiguity of its own, although it may be a problem only to a reader who is not only unusually precise, but also a bit of a pedant.
- There are many girls from poor families in the school.
Here, the other interpretation is that the school happens to have some affordable housing on its campus, some of which it rents to poor families who happen to have a larger than average number of daughters not all, and perhaps even none, of whom attend the school. Unlike with #2, I don't see a simple way of resolving that ambiguity.
In summary then:
In terms of capturing the meaning conveyed by #3, both #1 and #2 are fine in everyday use. For absolute precision, however, #2 is better than #1 because while both #1 and #2 contain some ambiguity, that in #2 can easily be resolved, it is less easy to do the same for #1.