It shouldn't cost much for a luthier just to re-glue the top. You don't have to get all the other stuff done which they will inevitably tell you needs to be done - at least not unless the instrument is un-playable without the repairs and the woman wants to play it or expects others to.

I believe luthiers use hide glue for violins. Elmers is fine for things that don't vibrate or have much tension on them, but not for musical instruments. Not unless they're doomed to hang on a wall and never be played.