We may have arrived at the key point of the argument. I can think of at least one good reason why it is good to specify a particular blood alcohol level. First, we achieve a strong degree of deterrence. I haven't checked the studies, but I suspect the actual incidence of a person having several drinks and getting behind the wheel is significantly lower than it once was simply because the penalties are so great. Deterrence of that sort is important because we can't exactly trust drunks to know whether or not they are good drivers under the influence when decision time arrives.
Back to the question of God-given rights. When I ponder what rights my creator may have imbued me with at conception, the right to drive a car on government roads after a few drinks does not score very highly on the list. I agree that the right to be free from unreasonable search and seizure is a good candidate, but when we get to that one we are simply quibbling over the details of how a DUI law should be implemented rather than arguing the greater issue of whether such a law should exist at all.