I'm going to put up a small nitpick right here rather than at the bottom, so that it doesn't look like I'm just adding on shit for no reason whatsoever, but Carthage isn't going to name a city "Hadiic Qart-Hadast" - and yes, I do know why you used Hadiic (
linko). They would've called it just plain old Qart-Hadast - that's what they did with Cartagena, and that's what they would've done there. Founding a new city as "Qart-Hadast" by Carthaginian settlers effectively makes it "New Carthage", just as founding the Carthage we all know and love by Tyrian settlers effectively made it "New Tyre", despite its literal name being closer to "New Town" - New Town implies the new version of the mother city. They wouldn't have called a place "New New Town", just as much as you wouldn't name a new New York as "New New York".
Carthage never had the manpower base to fight confidently back against the Silicians. Often, they held them back, but only just. Syracuse isn't going to fall to Carthage; it's the strongest state in the western Med.
Didn't Carthage have a fairly firm hold on Sicily later (around the time of Hammilcar)? That had to come from somewhere - probably mercenaries, but still.
You have to mindful that Carthage's dominance over Sicily was the product of Rome's rise.
Syracuse did fall to Carthage, practically, if not for Agathocles escaping. Here he doesn't escape.
A useful analogy (IMO) for understanding Carthage's situation in Sicily compared to the Greeks is to look at a much more recent in example, in the English/British and French empires in North America during the 17th and 18th centuries, where the Carthaginians equate to the French, and the Greeks equate to the British. Carthaginian Sicily, much like French North America, wasn't settler based but rather trade based - they had settlements, yes, and important ones at that (Lilybaeum, Eryx anybody?), but the primary goal was to control trade routes and as many as possible, not to export mass populations from the homeland, whereas the Greeks had left home in larger numbers to a smaller area, largely to escape overpopulation issues, and controlling trade was somewhat less of a priority than it was for the Phoenicians/Carthaginians. Trade is always a factor, but the Phoenicians and the Carthaginian settlements that followed them up spread out along much of the western Med to help establish control over the major trade routes of the Mediterranean, whereas the Greeks mostly concentrated their colonies in Eastern Sicily and Southern Italy; this led to a vast difference in population between the two cultures in the region. Now, because of the great population density contrast between Punic Sicily and Greek Sicily, the wars that were fought between the Carthaginians and Syracuse often found the Native Sicilians (whom were a substantial population) on the Carthaginian side, as the Greeks were pushing them back off their lands and whatnot (sound familiar?). As time went on, the Greeks gradually pushed the Carthaginians further west, but the Carthaginians always managed to hold their own in wars and fend off Greek attacks.
Now, Sicily was more important to the Carthaginians than New France and Louisiana were to the French - obviously, the other major bonus to Sicily, besides it being a great spot to control trade routes, was that it was sort of a buffer to protect Carthage itself, and Carthage did send more men and resources towards defending Sicily than the French did NA - so it isn't a perfect analogy, but I think it does help stress the point that having Carthage conquer not only Eastern Sicily but all of Magna Graecia and various Italian cities is almost as difficult as, say, the French conquering the 13 colonies.
Now, to apply this to your timeline...
I don't care if Agathocles dies - not only is Syracuse still a tough siege, even with Agathocles out of the way, but there is an enormous Greek population throughout the rest of the island that doesn't want to be conquered by Hamilcar, and nor does Hamilcar want to deal with an enormous Greek population as new subjects. And he
especially wouldn't go off and add more Greeks to his burgeoning empire that he's somehow put together, nevermind the great deal of difficulty he would have in being allowed to do that in the first place back at home, and how difficult it would be to conquer all of Greek Italy. Now, as I said earlier, the Carthaginians conquering all of the western Greeks in Italy and Sicily, and coastal Latium, is about equivalent (IMO) to the French conquering the 13 Colonies... imagine how much the American colonists would like to be French subjects, and that's probably not horribly far off how the Greeks might react to all being conquered by the Carthaginians (albeit less so due to the time period at hand), where they are ruled by foreigners and long time enemies at that. And now, with the Carthaginians invading Samnium... to continue the analogy, that's like the French then successfully conquering Spanish Florida and its Carribbean possessions after conquering the 13 colonies.
Carthage simply wasn't built to conquer like Rome, or even Syracuse, could - it doesn't assimilate, it doesn't have a huge citizen base. Carthage can get some breaks, but it isn't going to get enough to conquer eastern Sicily without any problems, let alone conquering half of Italy afterwards. The population is entirely hostile to them - they can win all the battles they want, how are they going to keep all those people to live with being under their rule? I'm not saying its entirely ASB for Carthage to conquer Syracuse - implausible for a long term conquest in this situation, yes, but not ASB - but it is basically impossible for Carthage to even want to conquer all of that territory that you have them conquer, let alone actually succeeding at it.