Stupid question if you ask me... first of all why exactly does she want to go back out with you?I would say don't go back out with her if she dumped you twice in one day.... and your friends are probably right, you deserve better.
How did you get dumped twice in one day? Sounds like something of a bad day. Figure out exactly why you were dumped, and see if you can work around it, or if it is likely to come up again.
Drop her at once, no calls, no conversation, no harsh words to her either, just cut her off. People playing other people happens all the time, unfortunately, is very common among the very young until they do some growing up and mature. She is using you as a convenience and is NOT someone to have anything to do with. Look elsewhere, plenty of girls out there who are honest and sincere, who are not players.
That'll teach the bitch a lesson!
Unless she stands you up as well, which would be hilarious!
Let us know how it goes.
Or maybe you need a few more years to realize you deserve more than being played.