The short answer to what the United Kingdom should do about Brexit and the border is: Nothing.
The UK has no interest in imposing any restrictions on imports from European Union member states, and especially from the Republic, nor in impeding movement of people within Ireland.
Whatever controls there are at present on non-EU migration into Northern Ireland and via Ireland into the UK can remain unchanged. (Does the UK rely on the Irish Authorities to do that anyway?)
Control of imports from Northern Ireland should be recorded by and monitored and taxed through Irish businesses and excessive abuse by individuals, if potentially causing a criminal offence in the Republic, would be a matter for the Garda.
The so-called difficulties resolve then into matters of internal administration within the Republic.
The question for Dublin is whether it will adopt a pragmatic approach to these issues and resist the bureaucratic whims of Brussels for unnecessary uniformity.
Christopher Swain, Maldon, Essex