You can change the executor of the will easily, if your eldest brother agrees that he does not want the position. He can simply sign a document stating that he
does not wish to become executor. Then you would sign a similar document. This would mean that your sister became executor.
If three siblings believe that your sister would be the best executor, hopefully you three will be persuasive with the oldest brother.
If your eldest brother insists on serving as executor, there is nothing you can do legally to prevent that. In theory you could bring a lawsuit against him seeking to deny him the executor's role, but that would be an exceedingly hard lawsuit to win. You would need proof that he was irresponsible and incapable of reasonably handling your mother's estate. More importantly, a lawsuit would almost surely generate family bitterness, always disastrous.
One technical matter. You refer to a trust your parents had. The person who takes over a trust after the trust creators die is called the "successor trustee." The person who handles a will is called the "executor." I think you want your sister to serve as both the successor trustee and the executor.