South Rim is pretty amazing and don't let anyone tell you that it's too much for kids that age. If your kids are troopers and athletic they can handle it. But if it were me I'd do that over two days and not all in one. All in one day is a major hike for even the most serious adult hikers. Someone else can give the specifics but it's got to be close to 20 miles round trip with a LOT of elevation gain for the whole round trip. My kids did it over two days and we camped at the top. I think there's only one spring to resupply water on the hike and it can be dry sometimes. There is no way around carrying a lot of weight if you need 2 days of water for 4 people.
If you don't do South Rim, Lost Mine is the next most beautiful hike. 6ish miles round trip I think. You can also head up towards the South Rim and enjoy some scenic spots with good views inside the basin without actually going all the way to the rim. The border crossing at Boquillas is a must-do item if the passports get done in time. My kids have been to the park several times and that has always been their favorite part of it. There is an option to walk into town from the river, but don't. Take the horses. Those guys need the money and there are several muddy creek crossings and a network of trails to get turned around on. The kids will like the horse ride. There are 2 restaurants in Boquillas and we always eat at the one on the right as you walk into town from the Mexican customs building. I like it and the food is good, but the other might be fine too.
I doubt anywhere in Terlingua shows the game. I could be wrong. There's the Starlight there but I don't remember any TVs on. The whole town is pretty much a place to escape TV and the real world. There is wifi in the Basin now. Not sure how reliable the signal would be for streaming, but it's there.