Code Golf: Forwards sdrawkcaB sdrawkcaB Forwards Forwards sdrawkcaB

TeaScript, 55 bytes 58 60 69 76 78 80 87 89

xO`a-z `?xl(#~-i&2?l:lv(),/ +/):Ld`SÀZn­ Û § «e Ò5s`

This is extremely short, I'm very happy with it.

The last ~20 characters may seem like gibberish but that's "Sentence must only use letters" encoded. All the characters have char codes below 256 so each are one byte

Explanation

xO`a-z `?  // If input contains only a-z and space...

   xl(#       // Loop through input 
      ~-i&2?  // If (index - 1 "unary and"ed with 2) isn't 0...
          :l,     // Leave alone
          lv()    // Otherwise, reverse string
       / +/ // Loops on spaces
   )

:Ld`SÀZn­ Û § «e Ò5s` // Otherwise... decompress and print  the error string

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Haskell, 141 bytes

r=reverse
f x|all(`elem`(' ':['a'..'z']++['A'..'Z']))x=unwords$zipWith($)(cycle[id,r,r,id])$words x|1<2=error"Sentence must only use letters"

Almost 2/3 of the code is for error checking. Seems to be the first real world challenge.

The work is done by unwords$zipWith($)(cycle[id,reverse,reverse,id])$words x which splits the input into a list of words, zips it with the cycling list of functions [id,reverse,reverse,id,id,reverse...] and joins the result with spaces back to a single string.

Thanks to @Christian Irwan for 2 bytes.

JavaScript (ES6) 122

f=s=>/[^a-z ]/i.test(s)?"Sentence must only use letters":s.split(/ +/).map((w,i)=>~-i&2?w:[...w].reverse().join``).join` `

alert(f(prompt('?','She sells Sea shells on the Sea shore')))