Unless I made a mistake converting dimensions, this is a mere 45*182cm, and 19mm strong. Which will, as LarryBud said, fit in ANY car, yours included. As for leather seats, simply putting a bedspread or such in between wood and seats will do fine (I do that when I drive wood, but usually with pieces that are 250cm rather than 180).
... it seems that you really want to cut that sheet in half, so... if you insist on doing that, I would do a straight cut. Not only is this easiest, but you can also use a couple of dowels, which greatly adds to stability and prevents you from going insane trying to glue those slippery bastards together in a straight way. Dowels are no fun with a slanted edge, though.
I recommend fish dowels (3 or 4) in this case (Edit: I just realized that the English word for these is "biscuits"), for which you can conveniently and extremely precisely cut the slit using the circular saw that you have (no free-hand drilling with an improvised jig into end grain as with ordinary dowels... what a nightmare!). That will ensure that the pieces fit together snugly and don't give you trouble shifting around while glueing. Plus, the dowels by themselves are surprisingly stable already.
The thing I'm talking about looks like this:
There are specialized litte joining saws for that, but you can do just fine wirh a normal circular saw. Simply adjust the parallel guide on your saw table so the cut lands approximately in the middle, and then you cut a notch into both pieces that are to be joined using the same setting. Voilà, identical matching notches, plug in fish dowel and add glue, press and done.
For a more favorable looks, be sure not to cut the notch all the way through, instead stop 2-3cm before the edge.
Back when I was in uni, I made a desk that went around the room's corner from a hardboard plate (like what people uses as work surface in the kitchen) joined with a couple of fish dowels and held together with a pair of screw connectors. No glue, just the dowels. Lasted for years, and it would support, well, a female student sitting on it, without breaking. No problem.