Intended as a perversion (using vile sorcery) of an opening spell. The successful effect would be to rend the victim's skin open and have the interior flesh spill outside it.
Imperative, Open! = Edro! Inside = ivil or ne Outside (adj/adv) eth Outside (noun) ar
Are any of these close?
Edro ethne! Edro ethivil! Edro arivil! Edro arne!
None of these are viable I'm afraid, you can't simply combine elements randomly.
The English phrase inside out is somewhat idiosyncratic, and if I had to translate turn inside out into Sindarin or any other language I'd sooner look into translating invert. However, in your case, it seems to be more literal, and I'd translate it as open the inside outwards: Edro en·ivil est!
(est ⪤ [ᴱ]Q. esta adv. "outwards" < √ET·da)
Of course the result is that this phrase in Sindarin would not sound particularly like whatever you'd likely use for "invert", somewhat losing the added connotation that you have in English. Not much you can do about this.