There are two typical answers, both of which have distinct problems. The more common one is that in an ideal Libertarian society, there would be no public roads, thus you wouldn’t have any law about driving drunk. What you would have is policy set by the road’s owner and agreed to by you in the contract you would sign to be allowed to drive on the road. So, you would have absolutely no government restriction on driving, but you would have private restrictions that could be equally or more severe than what we have today, but since it would not be government mandated you would have more liberty under the definition used by this sort of libertarian. Going into whether that variant definition of liberty is a useful and relevant one for actual people is a matter for GD.
The other major answer is to declare that creating a hazardous situation is initiation of force, and a Libertarian government acts against initiation of force and fraud, so you would have drunk driving laws. This has the problem that, as has been pointed out in this thread, ‘creating a hazardous situation’ can be used to justify a government passing a lot of laws not typically favored by Libertarians, such as anti-drug laws, anti-gun laws, safety and health standards for private property, anti-‘hate speech’ laws, or anti-pornography laws. Like the above, the details of this are probably more appropriate for GD.
Both of them underscore that, contrary to what the most strident Libertarians will say, the non-coercion principle does not provide an answer to everything.
Divorce is trivial, since ‘marriage’ in a Libertarian context is just a contract between two people, so the two people would simply use the clauses in their contract to break apart or would follow the normal procedures for dissolving a contract. Marriage is not a special institution set up by the state, but a particular contract between two people.
Child support is another really fuzzy area; the standard small-L libertarian response is that child support would be mandated by law, and would work something like it does today (though it would be simpler). When you get into cap-L Libertarians and anarcho-capitalists, child support gets really weird since the non-coercion principle doesn’t objectively define ‘child’ anywhere (is it someone over 14, 16, 18, or 21? “18 and not in college, otherwise 24”? or some other definition), and a child by definition would not be able to enter a contract with any agency to protect their rights; thus the parents would be obligated to pay child support, but this would only be enforced by whatever government/private protective service the parents signed on with, which leads to obvious problems.
