Helping Hercules, by Francesca Simon (new edition from Orion Press, September 2014, ages 7-9ish) is a fine example of mythological time travel for the young.
Susan is not a helpful child, not the sort of useful, pleasant child one actually wants to have around. She slams the door a few extra times when sent to her room (just to make her point), she doesn't think grown-ups should be the boss of her, she doesn't think it necessary that she be responsible for any domestic tasks. She's really more of an Ideas person (with her main idea being that she shouldn't have to help)....which her family hasn't learned to appreciate.
When an old coin takes her back to the golden age of mythological Greece, seven of the great Greek heros have a hard time appreciating her as well. Hercules doesn't give her credit for her clever suggestion of rivers as stable cleaners and Orpheus messes up his not-looking-back bit, despite Susan's coaching. There's nothing to be done about Paris (and Susan finds herself the target of annoyed goddesses, despite her best efforts not to be involved in the doomed beauty contest), but flying on Pegasus is rather lovely for her, though Bellerophon is a jerk. Perseus, however, is a decent sort, and he actually appreciates Susan's bright ideas (like using his shield for a mirror). Susan doesn't appreciate finding herself forced to take Andromeda's place (chained to the rock), but all ends well...
And here's Susan's reaction to being turned to gold by King Midas:
"This is boring, thought Susan.
This is very boring, she thought, some time later.
THIS IS EXTREMELY BORING! she fumed. I always did hate playing musical statues."*
This made me chuckle. Lots of the book made me chuckle--the Greek heroes (except for Perseus) are such stuck up snots, or else rather wet, like Orpheus, that it was nice to see them helped by/saddled with obnoxious Susan. And actually Susan rather grew on me--not that she Learned Life Lessons, exactly, from her time in the mythological past, but her brisk egocentrism and forthrightness made a nice foil for the heroic egocentrism she was paired with.
Francesca Simon is the author of the Horrid Henry books, and Helping Hercules would be a natural one to give to any kid who likes those books. It would also be a good introduction to the Greek hero stories for the kid who is a funny smart aleck, as opposed to a romantic purist mythology snob-- I'm not sure I would have liked the myths mucked with like this back when I was eight or so (although even then I didn't much like Hercules, and I had decided by that point that if I had to marry a Greek hero it would be Perseus, even though he made a Bad Choice at the end, so there you go). But then again, maybe I would have liked it--I was a Joan Aiken fan, after all, and there is something of an Aiken-ness in the saga of Susan....
Anyway, it's a nice, zippy, funny book, and I enjoyed it at this point in my life and it's easy to imagine lots of kids enjoying it too.
*do kids in the US play musical statues? My kids never have, and I was overseas at British schools (being very good at musical statues) when I was the right age for party games....