Final Update: We got up here about 3 hours ago. My SIL and I went out for some groceries and I brought up the booster. First things first, I had to ensure it had been purchased new. It is a Graco Big Kid backless purchased new, so that's ok. I will have to see him PROPERLY restrained in it to pass a final opinion. Then she said later, "Dad thought you were really mad about that picture." I said, "I was." We talked a bit and I explained that he has to have the shoulder belt always. I then talked to DS and simply told him any time he's in the car he can't put the belt behind him. He asked why and I told him its dangerous. I asked him, "You don't want to get hurt in the car do you?" He said, "No," and agreed. It's nothing that had ever come up before so he didn't realize it wasn't allowed, especially when the adults he trusted said it was ok. So anyhow, we are all on the same page now and looking forward to enjoying our vacation with them.
Update: I got an answer, sort of. I got an answer to one question (is he buckled and if so, why is he buckled wrong?). I do not have an answer to what seat it is or where it was purchased.
The explanation? He wanted to go to sleep but couldn't get comfortable so they suggested (SUGGESTED) he put the shoulder belt behind him. (Multiple things wrong here: 1. In a properly fitting booster, such as the one I sent, the belt doesn't rub and he can sleep just fine while properly restrained 2. The adults SUGGESTED it.) So yes, I'm angry and seeing red. In an accident, he would have been ejected and likely killed. This is NOT ok. Yes, we are going to be talking with them. This is not to happen anymore.
Is it just me or is it OBVIOUS that this child is not in a booster, or even so much as a seat belt?
He is SIX!!! I am so angry I could SPIT! And YES, I said something.
I'm sorry. I'm so upset, I forgot to include that this is MY child! He's with my inlaws. Yes, I'm livid. He has to be appropriately restrained in a child restraint. This isn't news to them.
Edit: I sent him up with an Evenflo Maestro (a one piece high back booster with no backless option). Though we can see an arm rest, it's clearly not his seat. I don't have a clue what seat he's in and it's clear he's not in a lap shoulder belt (all the cars they drive have lap shoulder in all seating positions). A lap belt only is completely unacceptable and not news to them. They were sent an appropriate restraint and are refusing to use it.