[Question] Smartphone < 180€/200$ good camera and 4.5" to 4.7"

[Sniper47]

The Xiaomi Redmi 3 might be a good match. It's 5.0", has a decent SOC (CPU/GPU), great battery life and good camera. Also it will be cute that both your wife and daughter have the same phone, though daughter will have momma phone and wife will have baby phone

It's also at a great price now at $125-130
http://www.gearbest.com/cell-phones/pp_367021.html

If want to step up one more step in camera, the Mi4C has Sony IMX258, same camera as what will be coming in the new Xiaomi Note Pro. This is a more powerful phone than Redmi 3, and 1080p display. The downside is that the battery life not as good as Redmi 3.
http://www.gearbest.com/cell-phones/pp_241901.html

These are both 5" phones, the Mi4C will be a bit slimmer, but both small. There aren't many <5" phones worth mentioning these days.