Re. school engagement - it's worth pointing out that sending out threatening letters really is not going to help if this is a situation. I mean, I am literate, university educated, professional, engaged with my son's education, he's never been late, I help with his homework and reading, he gets read bed time stories - my instinctive off the cuff reaction to the letter I got today was "fuck the lot of youse!" (I shall not act on that off the cuff reaction - but then I have the resources and experience of dealing with bureaucracy to know that a cool response is better). But imagine someone who is already disengaged with the school, who struggles with dealing with authority figures, who doesn't have practise in dealing with the system - I think it's fair to say you can take my reaction and multiply it a hundred fold.
So really, I think the "stick" is totally rubbish and counterproductive (and when it comes to carrots that depend on dumb luck rather than effort, which is precisely what a prize for 100% attendance is - well, frankly, they're totally rubbish too!)
Reward children for effort, and take the time to engage with parents on an individual basis. And use your discretion! (As an adult, I've worked for bosses who trusted me to sort my own work patterns out, and ones who were utter jobsworths - I know which ones I work harder for. And as a lecturer, I've known when to cut students a bit of slack and when to kick them up the arse - and I think I've very rarely got it wrong, in fact I've even had students thank me at graduation either for delivering a kick at the right moment, or for turning a blind eye when the rest of their life was going down the pan and they just needed someone to give them a break). Systems which work on a tick-box, one-size-fits-all approach are hardly ever fit for purpose.