I can fit Tutto (22" Large) on the floor in the back seat, (passenger side of my Honda Civic). Since the floor is uneven, it really doesn't roll around. But I place a tote back up against it on one side and that pretty much blocks it in. I have also placed in on the back seat on a piece of styrofoam, strapped in by the seat belt.
As far as lifting, I do not recommend you lift by the side brackets. I cracked a set and had to ship my trolley back to Tutto for repair. There are places on the metal frame you can grab if necessary. But as far as lifting, I use the top handle. The circumstance that lead to the brackets cracking was that the tote was briefly exposed to sub-zero temperatures when it was brought into the house from the car. DH carried it by the brackets not realizing the risk.