果たして、遺産を独り占めするためだけに、それだけのことを兄さんがやってのけるのか、わしも確信は持てん。
I'll translate it roughly as "I don't think he will go that far just to have the inheritance for himself." However, I don't understand the 果たして part: it seems that it can be a way of saying "as expected", but since they're theorizing, it seems odd to me.
The most prevalent meaning of this word today that you should learn is "...at all?" to emphasize the depth of doubt in question, although it's quite distant from its etymology.
３ （下に疑問を表す語を伴って）いったい。「果たして誰が栄冠を手にするか」
果たして……兄さんがやってのけるのか
Does my brother dare to do such ... at all?
Could my brother really dare to do such ... ?
While "as expected" is surely one of the meanings of 「果{は}たして」, it would not work in this context vey well. That meaning works only in a clear and declarative statement describing the expected result of an event.
The sentence in question, as its ending would indicate, talks about the speaker's uncertainty regarding the outcome of his brother's action. It is no declaration; In fact, the speaker is very unsure.
So, in this context, 「果たして」 means something along the lines of "really" or even "Would there be an answer (to this question)?"
"Whether or not my brother will really be able to pull off a job like that just to inherit everything, I have no idea."
really fits better than at all (from other answers).
”果たして” originally meant "as a consequence" or "eventually", but it is used in the sense of "if at all" to stress a certain doubt. For examples:
果たして彼が志望校に入れるかどうか、疑問だ - It's uncertain (at all) whether he can enter the school (university) he desires to enter.
果たしてこれが事件の決め手になるか、どうか？ - It's questionable (at all) if this can be a decisive clue to settle the case.
果たしてイランは約束を守るか、どうか? - No one can tell whether Iran will keep their promise.