awkward driveway curve has cars nearly colliding with house, how to mitigate?
My suggestion is to add to the size of the concrete drive way in the following manner: 



This gives you the option of backing up out of the car port in the new area toward the rear yard. Then you can drive in a forward direction which would be far easier to navigate by the truck and the corner of the house.

Additionally the part added onto the side nearer to the street view will allow the truck parking area to be moved over a little to alleviate the congestion posed by the parked vehicle in its current spot. 

Adding onto existing concrete like this is certainly doable but there can be some downsides including looks and joining the new to the old slabs. If those are of concern to you then you would be looking at taking out a good portion of the existing slab and replacing with all new. Cost factors can be a good aid in the decision path.