What exactly are the tools in question—hammer drill, impact driver, or impact wrench? They're quite different in what they do. It sounds like a hammer drill and an (impact?) driver maybe. A hammer drill has a standard drill chuck, with adjustable jaws; an impact driver has a locking hex chuck for driver bits (that can't be adjusted for size); and an impact wrench has a square socket driver, usually 1/2".
Neither a hammer drill nor an impact driver is likely to do very well at breaking lug nuts free. Either one probably could spin them off once loosened a bit, but the impact/hammer part is not really all that useful there.
The HF hex driver bit to square drive socket adapters are not terrible, but I don't know that they'd hold up to sever usage. Certainly for spinning the nuts on and off they work just fine.