"My dd only told us tonight. We were not livid when collecting her, we had no idea she had been left alone."
- yet another inconsistency. You said early on in the thread, that you were shocked and angry to find your dd left outside 'on the street' (or was it playgground?!)
You now say that actually, you didn't notice anything untoward, except that your dd looked like she'd been crying (which the tutor, who was clearly at the school then, dismissed as her being upset by your lateness)
So, you went off and did the rest of your busy Saturday, and it only emerged at bed time that your dd said the tutor had gone to get her lunch. You then surmise from this that the tutor 'must have walked two streets away because that's the nearest place to buy food'!
Your story is full of inconsistencies from start to finish. Why say earlier that you were upset at her being left unattended when you are now saying you didn't even realise anything was wrong?
Also - you still haven't explained why you think the tutor should have phoned you to explain her movements (which may have been inside the building still, as you only have your dd's assumption that she went off two streets away) yet you couldn't be bothered to call her to explain your lateness?
Finally, none of the few people on here who have tried to defend your actions, have actually explained what this woman was supposed to do? What if she had children of her own to pick up? What about her parental duty to them? Or do they just go hang because you mistakenly think her duty to your child is greater?
She had no idea when you might turn up. I have known teachers (and I'm talking about real teachers in school situations, not some tutoring arrangement) who have waited with youngsters for well over an hour, sometimes late in the evening when a school trip returns, and parents can't be bothered to arrive on time and can't be bothered to contact the school to say so. Obviously in these situations, there is normally more than one member of staff who can wait... but you can see the problem can't you? What if a teacher has a trip arriving back at 9 pm, and has arranged to (for example) pick up her own daughter from an evening out at 10pm. What does she do if she's still got school kids waiting to be collected, and has had no communication from the parents? Leave her own daughter standing on a dark street corner waiting, because the parental duty of care to her takes lower priority than the parental duty of the parents who can't be bothered to pick up their kids? 
OP - it doesn't matter how much you rant and twist and turn your story - YABVVVVVVVU to offload the entire responsibility onto someone else, when it's you and your DH who messed up, and you wouldn't stand a hope in hell of taking any action against this tutor.