I have a dog rescued from Romania, coming up to our third anniversary!
I specifically wanted a dog from the local area (Yorkshire) and after much research went to a small rescue centre near Rotherham. (HYPS, if anyone's interested). They often have a lot of Staffies and Sighthounds, it seems they're often the ones abandoned and ill treated. My choice was a small mutt, who wasn't super - cute or squishy or anything exciting ~ but mine from the moment we set eyes on each other.
I've been very lucky. Apart from eating a chromebook cable on Day 1, he hasn't put a paw wrong, and is very gentle.
The charity takes enormous care with their adoptions, and very often specifies that they won't rehome to families with very young children - just in case.
So I'd hope the charity your daughter's looking at is just as meticulous about assessing prospective families.
As to cages, provided they're a decent size for the dog, have comfy bedding and water in, they can be perfect for a dog for time-out time, especially for a dog coming from a traumatic past; to a dog it's not a prison, it's a sanctuary.