We have a Snoozer too. Ours is the smaller one since I only have KS. She loves it and it has been a lifesaver! The tether seems super sturdy to me, never had a problem. My only 2 complaints: one, we got ours in the pink vinyl fabric. I thought it would be easier to wipe down. Although it is, I did put it in the wash one time and the vinyl cracked in a few places. Second, the foam underneath, on the sides, could be a bit stronger. KS is only 4.8 pounds and she loves to prop up on one side. Ours is already sort of bending and showing its wear after only a year. But I would buy it again if I had to, but I'd change the outer part to something besides the vinyl.
Congrats on your new car!