I dont know the original sentences but...
Dudley couldn't touch the letter even one time.
so in this scene, his uncle(おじさん)has the letter, and Dudley tried to rob the letter and read the letter but he couldn't both of them.
if he could rob the letter but he couldn't read,
he could get the letter but his uncle get it back.
and if he could rob and read the letter halfway but he couldn't read all of the letter.
and your question, 奪って読もうとしたが there are two verbs, and ~が.
"奪って読もう" including (奪おうとした：tried to rob）and (読もうとした:tried to read).
and you can estimate to failed some action from 〜が.
there are two possibility, Dudley couldn't rob, and couldn't read. or, Dudley could rob but couldn't read.
(in the case could read but couldn't rob, if u could read, Dudley have to rob the letter.)
and next sentence Uncle hold the letter higher place. that means he holding letter, if Dudley could rob, there are the expression Uncle could get the letter back.
but the original sentences there is no such expression. so that means Dudley failed to rob the letter.
so, first question, yes you are correct.
and next question,
if Dudley could get the letter, but couldn't read. and keep the next sentence like that.
in this case Dudley couldn't read even one word of letter.
in this case Dudley could read halfway but couldn't read all.
if you want to change, you should explain the fact that uncle get the letter buck.
im Japanese. so, im sorry for some mistakes of English.