DD is a mixed bag, and it depends on whether it really is nap time, how busy the road is etc.

BUT one trick I have, is to put her straight onto the boob (literally there in the back of the car) and carry her into the house feeding (obviously having unlocked the house first) and let her feed for a while and then transfer to the cot.

Never even tried car to pram...but I used to do car to sling a lot and sling to cot has always been easy.

HTH