If you read the instructions that come with the blue or gray tanks, they want you to fill the tank via a garden hose fitting that they supply.
And then they suggest you dump using the shorty 3" "stinky slinky" that comes with the tank.
If you follow the instructions, it pretty much rules out totally dumping black water because the fill hose is way too small for uh, ah, solids.
When dry camping for long periods, I have successfully been able to drain down some of the liquid from the black tank by opening the valve just a tiny bit. It's do-able, but care is necessary.
I was at the dump station once, and watched a guy try to dump his blue tank with the 3" hose only partly attached. It took him 3 tries to get the hose properly connected. Of course, by then the stuff was all over the place. And he had dumped his black tank into the tote. Not a pretty sight. I used a different lane that day.
A suggestion... The manufacturers provide a second garden hose fitting on the tank with a cap. They instruct you to loosen the cap so that air can escape as the liquids pour into the tank. That can deposit some pretty foul odors around and under your trailer. I took an old section of garden hose about 10' long and rigged it so that the male end is about 11' off the ground by hanging it from the TT's gutter with some string and an S hook. The female end I connected to the tank. Now, when I dump, the odors are vented up above the trailer in the same fashion as the vent stacks on your gray and black tanks.
Also, it is not suggested that you leave the valve to the tote open. Let your gray tank fill, and then dump into the tote and close the valve again. If you leave the valve open, you are pretty much guaranteed to forget it until it overflows. Pretty much the same rule as when hooked up no a sewer site. Let the gray tank get at least partly full so that you can flush the hoses after dumping the black tank.
It's probably wise to be very conscious of the size of your tote and the size of your holding tanks. You can't squeeze 25 gallons into a 15 gallon tote. I would much rather under fill the tote and make two trips to the dump station than over fill it and have to deal with the mess.+
As for carrying the tote, I usually use some heavy duty bungies and tie it down on the very top of the stuff in the bed of the truck. It's light weight and easily loaded or unloaded if I need to get to something else in the truck.
If we're loaded to the gunwales for a two or three week trip to the Adirondacks, I sometimes toss it in the boat. It weighs so little that it won't affect the loading of the boat. Darned thing wants to sway if there is too much weight rear of the axle.