What is more harmful in a car crash - restrciting movement or allowing some movement to reduce g-force? Sorry if I haven't worded the title very well, feel free to improve.
Let me explain before I ask my question...
We have purchased a car carrier (small version) for our dog and also purchased some straps to secure it to the seat; however we have noticed that even though it is secured to the seatbelt it is still a little loose (you can move the carrier forward a bit before it attempts to prevent further movement).
I have heard someone else that has used these same straps state they have instead put the straps around the whole back of the seat rather than use the seatbelt and they have stated it is now much more secure/tighter against the seat and hence prevents much movement.
So my question is - which method is better/safer?


*

*Securing it around the seat, to me, seems like it may be a better option as it helps prevent movement, but I'm wondering, because of this lack of movement, would our dog now have to sustain more g-force?

*Securing it to the seatbelt, to me, would seem to propel the carrier forward on an impact until it is stopped and then our dog would be thrown forward into the front of the carrier in a more "jerky" fashion then when secure but may not have to sustain as much g-force!?


As a side note, if it matters, we have been told by CPS that the straps we purchased are not strength rated; which I assume means they have the potential to break at high points of impact, but we are open to purchasing better ones if need be, but I am also cautious about using straps not specifically made for carriers as I have heard using seatbelts around carriers can potentially crush them.
 A: The short answer to the question as posed in the title to your post is both.
The purpose of the seatbelt is to restrain you so that you stop with the car thereby making your stopping distance the same as the car and greater than if you had no seatbelt. Without the seat belt your inertia keeps you moving forward at the same velocity until you impact an object in the car which then stops you. You are then at the mercy of how much "give" the object has since that will determine your stopping distance.   
A crash which stops the car and driver must take away all its kinetic energy according to the work energy principle which states that the net work done on an object equals its change in kinetic energy, or 
$$F_{ave}d=-\frac{mv^2}{2}$$
Where $F_{ave}$ = the average force you experience.
$d$ = your (and the vehicles) stopping distance.
$m$ =  your mass
$v$  =  your (and vehicle) relative velocity with wall before the crash
The vehicles crumple zone, seat belts, and air bags are all designed to increase your stopping distance and/or absorb the energy of the impact.
On the other hand, seat belts with a moderate amount of stretch further increases the stopping distance of the occupant, additionally reducing the average force experienced by the occupant while still restraining the occupant from impacting the objects within the vehicle.
Hope this helps.
A: A body in motion has an inertia of motion by virtue of which it tries to maintain it's previous state of motion(both speed and direction). For example it is noticed that on suddenly applying brakes to stop we are jerked in forward direction which is due to the inertia of motion.
Now when we are in enclosed space we must take care of the fact that if we don't stop, relative to the nearby objects,  then it is quite probable that we may get hurt. So what to do then? Answer is to somehow attach ourselves to the surrounding so that when they stop our body stops with the them. But there is another problem which is of the case that on making our body to stop suddenly by applying constraints causes a lot of force on our body which can cause minor/sever damage and can be lethal. 
So what should we do then? 
The right thing is the case which is somewhere inbetween i.e., to make our bodies stop in such amount of time that a comparatively lesser force acts on us but we stop in such distance that our head or other part doesn't collide with the nearby object. So my suggestion is to do the thing in which both are satisfied. 

$$\pmb {\underline {\text {Further Reading }}}$$


*

*The Statistics: Car Safety and Pets in America

*How to Keep Your Pets Safe When Traveling

*Pet Travel Safety - How To Travel Long Distance | American Red Cross

*Travel Safety Tips | ASPCA
A: When your car drives head-on into an unyielding obstacle, the front end of the car will absorb energy by "crumpling." The relatively rigid passenger compartment will take somewhat more time to come to a stop than the front bumper will take, and so the passenger compartment and anything that is rigidly attached to the passenger compartment will experience a lower peak acceleration than the front bumper will experience.
Instead of a car, Let's imagine a bus that runs head on into a wall while traveling at 60 miles per hour, with your dog on the back seat.  If your dog is not strapped in, then as the bus starts to crumple, your dog will continue at 60 miles per hour, flying through the air, until it impacts the front of the bus, which likely will have come to a compete stop by that time. But, if your dog is strapped in to the back seat, then it, and the back seat, will slow down more gently while the front of the bus is crumpling.
The difference might not be as great in a shorter car, but I'd still rather be strapped in than not.

P.S., When the police officer looked at me, sitting unhurt on the grass next to the wreck of my car he said, "I don't need to ask whether you were wearing your seat belt." I guess he'd seen enough people who were and enough who weren't to be able to tell the difference.
A: I refer you Bob D's answer above for the physics.
At the moment of impact, the carrier will move forward until it reaches the limit of the restraining straps. The straps then undergo a deformation (elastic and inelastic), over the scale of a few centimetres, that decelerates the load. This process is the same whether the straps are loose or tight because the load is moving at the same speed at the moment when they reach their limit and begin to bite.
So it doesn't really matter if the straps are very tight or not. As long as they not so slack that the carrier can move forward enough to impact something in front.
