I could largely post the same joys over my 2010 LR4, though I had no accidents in it. Bought in 11/09. We, too, have 5 kids. I used all aspects of our LR4, including our hitch (though only for attaching a bike hitch bar). Middle row folded and put back up daily, 3rd row folded at least weekly for transporting stuff...
The only issues we had were some insignificant things, like the post between the third row seats getting knocked off within weeks of ownership (they just had to secure it back on, though it always wiggled freely if grabbed). Eventually, the spot that receives the seat portion of the third row seat portion when folded flat locked up on one side and wouldn't let the seat lock in.
We did end up with something terribly odd going on that started right at about 24 months of ownership. The car wasn't engaging in drive for up to a minute first time in the morning, only when cold, and only sporadically. Then, it started... falling out of drive, is the only way I can describe it, where I'd be driving, not take it out of drive, but after breaking hard the engine would only rev when the gas was pressed. It was only for a couple of seconds, but still, totally not okay. They tried resetting bunches of software, gave it back, said it was fixed, then midway home on the 3rd day after having it back the engine shut off, battery and engine lights came on, wouldn't start. Had it towed. Though we are only half way through the warranty, we traded in for a 2012 a couple weeks ago.
On our breaks and rotors, we never had them replaced. We were right about 23k miles when we traded in. The dealership was pressing me to have it done, saying that they are generally in need of replacing anywhere between 10k and 21k miles. I thought that to be a funny spread, considering I was at 22k when they were pushing it. Also, I don't drive gently, and the majority of my miles were city miles. They assured me my light would come on when they hit the absolute-must-change-now point.
Oh, and the tires needed changing. The tread was getting pretty bad, which again, they said was totally normal for this car, generally seeing them need to be replaced around 18k. Seems interesting. While we generally only keep our vehicles for 2-3 years, we have never had tires be in such bad shape by 2 years.
Anyway, we really did enjoy the LR4. We love the car that seats the 7 of us, but still drives like a sedan and not a boat. Love it even more than we liked the Lexus GX470 we had back in 2005 (aside from that, for our big brood, we've had 3 Yukons and an Escalade.
Far and away, for off roading, our favorite vehicle is the Ford Raptor. Nothing compares! But for hauling our family around, I love our LR4. Your pictures from your accident are fantastic! Cool that you sustained so little damage. Your bag didn't deploy, I take it? How much of a **** did you feel being rear ended at that speed? Do you recall, was your foot kept firmly on the brake for impact or had you let off at all? Just curious, super cool that you had a tiny bit of damage! We had a little off-road oops in our Dodge Power Wagon, to the point we thought we were going to end up totaled. We ended up landing on the front mount winch and it took all the shock into the frame... no damage! It is amazing what the right impact on the right spot can do, or not do.