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I had a Mju II and sold it on here, actually. She's after something she can control more so a compact sir, as you say, might be a good way to got. It's going to be lighter than the Zeiss (which I once swung into my then toddler daughter's head, while it was slung over my shoulder - don't think i've ever felt a shoddier parent than that!).
@mrboulard how useable are those Rolleis? Because of their size, i always assumed they'd be a bit fiddly to use, but I've never had a chance to try one out.
Olympus XA ? Should be able to get one of those in budget with the flash and case. Olympus Mju II if you're lucky ?
Otherwise Nikon L35AF. Hipster tax starts inflating prices for compacts after that
Alternatively, you should be able to get a compact SLR with lens such as Olympus OM series, Nikon FE/FM, Pentax ME Super etc in that budget also
Edit - Also Olympus 35 RC/RD/SP series, pretty much a more advanced Trip