Some games require more buttons than one of the included controllers (joycon) provide. So with the included ones that would make the game single player only. As a rule of thumb, any game where you can move in 3D requires both joycons.

Mario Kart is great. It can entertain for a long time if they like racing. The two joycons are sufficient for two players.

Here is the list of the best Switch games in general. Maybe something catches your fancy?

The initially included controllers are sufficient for most games, but I’d highly recommend getting a second pair. If cost is a factor, you can look at brands like PowerA to get cheap controllers that will function on most games.

Games are a little harder to recommend without knowing their interests and your limitations. Super Smash and Mario Kart were already recommended, and these are solid picks.

If you’re looking for co-op games, Luigi’s Mansion is a good choice. I also love recommending Snipperclips, a cheap competitive and co-op puzzle game, and either Donkey Kong Tropical Freeze or Kirby’s Star Allies depending on your kids’ interest in aesthetics.

Boomerang Fu, Super Bomberman R, and Towerfall are slightly higher in the violence scale and (possibly) lower in per-sitting playtime, abut are solid “party games” that aren’t too gorey or violent.

Games like Pokemon are good time sinks if you need them to be occupied for long stretches, though are not as multiplayer friendly when on a single console. Warriors games (either Hyrule Warriors or Fire Emblem Warriors) are great co-op time sinks with lots of grindable unlocks for them to find, but the game will absolutely get stale quick if they’re not drawn into the hack n’ slash formula they use.

Some hopefully helpful answers:

1. the included controllers should be fine for the trip. They are called “joycons”, so that is a good way to distinguish them, especially when talking about multiplayer. They aren’t the most economic things in the world though, so you might want to consider getting two pro controllers, but if you decide your kids are going to make do with the included hardware, they should work fine.

2. The USBC port is indeed on the bottom, because this is where the TV docking station connects to it. The best solution is to have some kind of standh to ensure there is enough clearance to run the cable. Idk what its power consumption is, so I can’t be much help if you plan on charging it from your car. I guess they’re are licensed car chargers out there, although it seems like the current draw is a bit high for that sort of thing.

3. As for game recommendations, Mario Kart is pretty near the top of the list. I think for 10-14 year olds, the real killer app is going to be Smash Bros. Ultimate. It’s a game where you fight other players using characters from other popular video game series. It’s all about knocking each other off a stage though - no blood, gore, or realistic guns. Just be aware that they charge extra for a lot of the characters in the game, but it comes with a pretty wide selection of them with just the base game purchase.

Another bonus rec for more of a family games situation: clubhouse games: 51 worldwide classics is a really great and well made gaming collection. It can be surprising hard to find a good version of this type of thing because a lot of companies will try to take advantage of parents and families and rush really shoddy versions of monopoly or whatever to market. But the clubhouse collection has gotten a reputation for being very well done. Just to be clear though, this is a recommendation for if you want to have some kind of family board game night using the switch, NOT a recommendation for something 10-14 year olds would want to play on their own.

Technically the included controllers are enough for 2 people, but they’re quite small when used individually. I’d suggest a 2nd pair.

The charging port is in the same spot on both the OLED and original. There are probably some 3rd party docks out there that double as a stand which don’t block the screen that might work for charging while playing.

Mario Kart, Smash Bros, Mario 3D World, can’t really go wrong with multiplayer Mario games. The new Zelda (Tears of the Kingdom) is great, but single player — however it can be great fun to watch others play as well so taking turns may be fine