why is emma frost older in x-men first class but younger in x-men origins?

Fox has messed up the stories. Emma Frost should not have been in X-men origins. The mutant in origins has a similar ability (diamond skin) as Emma Frost but Emma Frost did not gain that ability until much later.

I don't know why Fox decided to put her in the Origins movie.

For the same reason Charles could walk at the end of Origins but was paralized at the end of First Class, or that they had 3 different girls of all different ages playing Kitty Pryde throughout the 3 movies. Continuity, plotline differences. They don't ever really think of prequels when they're making a movie. Luckily, however, the X-Men universe is so diverse and they are always switching things around in the comics that it works.