The word is
Hear ye, hear ye, my first is the, Arabic!
As @Amoz pointed out, "the" in Arabic is "al".
Hear ye, hear ye, my second is money, I don’t know why!
Literally the word "money" without the "y", clued by "why" (as @Amoz pointed out)
It is for sure simpler than we thought.
Also, the hint "Thou hast one, but one’s not done" could clue "one", which is part of "mone", and it is "not done" because another letter (m) must be added to it.
Hear ye, hear ye, oyez, oyez, my last is number one (hehehe) with a stick!
The childish laughs (hehehe) at "number one" clues the letter "P" because "number one" means pee and "number two" means poop. A "P" with a stick is an "R". A child might laugh when they hear the phrase "number one" because they are thinking of the meaning above. It is just a more polite way of speaking to your children in public, i.e. "Do you need to go #1 or #2?"
Hear ye, oyez! My whole gives out my middle!
Altogether we get ALMONER, which is one who distributes alms.
Alms is something (such as money or food) given freely to relieve the poor.
The hint "And the ending is DEFINITELY what thou hast not wrought" could mean that the "ending" (referring to the final complete word) references something that you didn't make/create, but instead something that was given to you (alms).
PUZZLE POSTER NOTES (by @someoneinexistence)
Okay, that’s a wrap on this riley! All I wanted to say here is that most of the hints were DOUBLE PLAYS! such as “And the ending is DEFINITELY not what thou hast wrought” meaning “oh, @Amoz was wrong” and that “oh, the ENDING was wrong”. Oh, and also the reason above. “Thou hast one, but one’s not done” is both what he said AND a reference to the fact that only one in @Amoz’s answer was right. NOW GO SOLVE MY OTHER RILEY! (lol)