Check the instructions for your specific model of child safety seat. Many don't really use the shoulder strap - it is secured down across the lap to keep it out of the way. My granddaughters safety seat had a five point harness as part of the seat. The seat was secured to the vehicle with the lap belt - and REALLY cinched down to prevent movement. IF the car was equipped with the additional strap that comes over the top of the seat back, that could be clipped on also but was not required. Not all vehicles or seat positions have those so many car seats do not rely on them. The standard seat belt shoulder strap only came into play when we converted the car seat to a booster seat. If your grandchild's car seat is similar to ours (or if you buy one with the same set up), then the front facing dinette seat with standard lap belt should work without alteration.
If the child is very young, the non-driving adult should sit with the child to help with entertainment. There are many magnet travel sets and games that keep all the pieces pretty much in one place. We used a DVD player and headphones on a long air trip so Chloe could watch movies (< 2 yrs old at the time) but these days you might be able to get what you need at your library. Ours have pre-loaded tablets (no wifi needed to play) with lots of games, play aways (audio books that you plug headphones/earbuds in) and lots of kids books on CD. Chloe likes to get the book and the CD so that she can follow the story while it reads to her (though she objects to some of the voices - the deep, gruff voiced guy speaking as a girl was especially grating to her). I recommend a "kid bag" that the child has free access to with all the travel toys you take. You can include a no spill cup and snacks. Chloe LOVED being in charge of "HER STUFF". Avoid crayons and other things that roll off the table unless you want to play pick up repeatedly during the trip. Now that Chloe is bigger, she uses a lap desk from Michael's that has two deep pockets on each side so her book, water pouch, drawing supplies, earbuds, etc., stay in the table. It didn't fit over the arms of her full car seat though so it wouldn't work for that. A car seat cup holder WILL hold crayons and such in a paper cup.
Enjoy the grandchild journey! Chloe considers the PC to be HER camper-house and loves traveling in it. Read up on Fairy Houses before you go. That was Chloe's first activity when we hit camp - scope out a good "building site" and gather materials; pine cones, acorns, pine needles, rocks, sticks, moss, cool leaves, etc. We've left fairy houses in many campgrounds in many states throughout the north east US.