Just to set a few things straight:
A.) Suitcase nuclear weapons are real. Developed during the cold war as 'Atomic Demolitions Munitions' they are very small, known only to weight about 50 pounds such as our W-54 davey crocket. They use either a relatively inefficient gun type sub-critical fission assembly or a more efficient oblique implosion type assembly as was likely used in later small warheads. Also it is likely, although not acknowledged that both the former Soviet Union and US maintain smaller warheads for spec ops reasons derived from the primaries of modern two stage fusion devices.
B.) Warheads, fissile materials and all release very low levels of background radiation, it's the daughter particles and associated radiation produced during a runaway fission reaction during detonation that are highly radioactive. Very few long lived daughter particles are produced from the fusion stage of the device, thus warheads that acheive bigger percentages of their yeild from fusion are 'cleaner' then pure fission bombs. This is why there is significant research being done (I would expect anyways) towards developing pure fusion, or fallout free bombs. I'd wager a years pay this is one of the hidden motivations from building the national ignition facility.
C.) It is probably possible to build a nuclear powered car, well or tractor trailer at least using a liquid potassium or liquid magnesium single stage cooling loop and MHD coupling (similar to the SNAP-1 reactor built for satellite use in the 60-70s), but it would be heavy, expensive, and if you think the environmentalists are pissed about your SUV just wait until they see your 15megawatt pride and joy.