Teams staying in hotels for home games
There are lots of reasons this is done. Now note, not all teams do this and some only do it for some games; very important ones, cup games etc, or games with an early kickoff, say mid afternoon. Reasons
a) Makes it easier to keep an eye on players, to ensure they get adequet rest and nutrition…you don’t want your star player underperforming because he was out having a later dinner with his wife and had a few too many. Also permits the coaches to hold pre-game discussions withe specific players.
b) These days ite reletivley rare for a team to actually have its practice fascility at the stadium… most of these are seperate from the stadium an in some cases far from it. In workplace parlance, the players “office” is their training ground and the stadium is just a place off site they have to visit a few times a month. So their homes will be in relation to the training ground NOT the stadium and it may well be easier to stay overight in a hotel nearby.
Flying home right after a game
The schedule is released months before the season starts, so by the time a team is expected to play at xyx venue, the movement plan is all ready. And the time of a teams departure depends on that plan. Remember its not just the players and coached who travel, but the support staff and a lot of equipment. Moving that at night is easier than doing the same in the morning…in fact typically by the time the game starts most of the stuff is already packed and ready to go, most of it is already moving to the aiport during the game, except the players kits of course, which will be packed up and moved right after.
The players travel first or business class which is less tiring than economy class and in most clubs the day right after a game is either off or has only light training.
Lots of Youtube behind the scene videos available.