It's a shame about the clock as you can get mains powered ones so you wouldn't have to worry about charging. Which ever one you get make sure to buy a decent memory card for it (don't buy it with the device as places charge a big premium for relatively small cards) and the biggest capacity it will take as old footage is overwritten when it fills up and if your not able to download it regularly you might miss something.
To avoid getting 'caught' downloading it at the home simply buy an extra memory card and just swap them over and download the footage at home.
You could go with something like this
https://www.eyetek.co.uk/hidden-camera-usb-charger as it's mains powered motion detection (so will fill the card slower) and everyone has a usb charger these days so will be inconspicuous. This might be worth a punt
http://www.ebay.co.uk/itm/1080P-HD-Spy- ... 2548.l4275 but won't be full 1080p probably upscaled so check footage and area covered before putting into the home. The disadvantage is someone by borrow the charger to charge their phone!
There is even a table lamp
https://www.eyetek.co.uk/lamp-camera-dvrSmoke detectors are good as they can be placed in the centre of a room and give a wide coverage but these will be battery powered same as PIR detectors. HOwever if in motion mode they should have a decent standby (no recording time).