oh Lisa, it is so hard when somehting goes wrong on your 'time off'
do try not to let this get bigger than it is though. you say your parents have looked after them before - presumably all went ok enough then? it must have done for your parents ot even manage to forget the important stuff (assuming they 'accept' the ASD etc?)
how old are your girls? funnily enough, we found it easier when dd1 was little (up to about 4ish) and dd2 a baby to go out - dd1 not ecstatic about the idea, but accepted it ok. but then the years in between them and now - so from dd1 being 4 up to this year (7/8), it has been a lot harder, because dd1 has been a lot more vocal about her dislikes, and dd2 has picked up on that and also then been upset - vicious circle...
I always do a list of what needs ot be done - I have done this for family, for my best friend (who is an angel and doing loads of childcare type things for me at the moment), even for tutors from dd1's last school, who new her really well.
I list:
what needs to be done (and when - dd1 obsessed with times), down to the last detail, if it is important (eg what words/phrases to use, or what order to give drinks at bedtime/which cup etc)
how to do it (whether the girls help or not, if they have drinks in the kitchen/playroom/bedroom/whatever)
and also, crucially, a list of tiny little signs of unease, and what might be able to be done about them (leave alone to work it through, bung on favourite dvd, move straight to damage control of favourite snacks, etc)
whoever looks after them already knows all this stuff (have seen it a million times before, heard all the routines etc) but for my own peace of mind I write it down, andthen if there is a situation, the info is there for them. I find it hard enough to think my way through stuff sometimes, let alone people who don't have to deal with ti every day.