So... how are the people of Rome going to take the death of Commodus? Sure the main characters and the movie audience might know how much of a monster he is but from what see he very much a Villain with Good Publicity to the average Roman. To all appearances Commodus was killed by a pre-planned coup by Maximus, Lucilla (who 'reveals' herself to be Maximus's lover by rushing to his side when Maximus is dying), Quintus and possibly Gracchus. Sure they might say they are following the wishes of Marcus Aurelius but he is inconveniently dead.
Given that the new rulers are also in command of the entire army (plus Commodus having apparently never been particularly popular with his commanders), it probably doesn't matter what the people think because thinking against the killing would likely lead to becoming equally dead. Alternately, they wouldn't care as long as the new ruler didn't suck at his job. They didn't elect Commodus, so they probably wouldn't be that ticked off at his death.
Actually, the common people's opinion of Commodus seems to not be that good. Sure, they love the bread and circuses, but when Maximus rises in defiance, they side with him rather than Commodus, as a few scenes show (their cheering forced Commodus to spare Maximus in his first Colosseum fight, people called him "Maximus the Merciful" for sparing a gladiator that Commodus would have had killed, and the play with Maximus defying and defeating Commodus all being evidence of that). In fact, the only reason Commodus didn't have Maximus killed outside of the arena was because of how popular he was.
Where does Maximus live exactly? In the opening of the movie, he is with his army in Germanina( Western Germany). He gets away from his would-be killers, steals a horse, and rides ...home. Home however, is implied to be Hispania(Spain). At the time he leaves, he has a horse, part of his uniform, a sword, and presumably, no money or food. Yet he rides across part of SW Germany, all of Southern Gaul(France),maybe?, crosses the Pyrenees mountain range?, then home to (somewhere) in Spain. Just in time to find his murdered family still hanging in his yard. This all happens very quickly(in movie terms), yet he is just behind the team sent to murder his family. I dont know how long it would take to ride a horse from Germany to Spain, even if using the excellent Roman road system, but I think it would take some time, especially if he is a fugitive.It gets more confusing, after the events at his estate, he seems to not have bothered to obtain any supplies or gear, clothing, anything really, and next we see, he is in North Africa and is a ragged looking prisoner at that. Not all that far from Spain, but still across the mediterranean sea. If anything one could likely have made an entire movie *just* about his ride from Germania to Spain alone for all the time and effort it must have taken.
He lives in Spain. The director's commentary actually mentions this particular scene. To quote the commentary, they originally planned to show more of the trip, but the realization that it, indeed, was worthy of a movie in and of itself, lead to them simply "trusting in movie magic" to get him home. Also, even if Maximus left sooner, he probably had to travel through the backwoods and off the main roads where he might have been seen, given he was (to his own knowledge)a fugitive. The soldiers didn't have that problem. This troper is more surprised he seems to have arrived only a few hours at most after the soldiers left.