For UKIP to implement the said proposals, they would not only "have to leave the EU" as they put it in their own vision of things, but they would effectively end the Common Travel Area
as we know it. Ever since the partition of Ireland nearly a century ago, there has never
been a permanent residency or passport check on those crossing the border between Northern Ireland and the Republic. Not even during the height of the troubles - there have been checkpoints set up on border roads in the past for customs & security purposes (not only the troubles on both sides, but also more recently in the Republic to prevent the spread of foot & mouth disease), but that's it as much as I'm aware.
If UKIP wanted to implement control of the country's border as they propose to do so, then if the Irish Republic was to remain in the EU (highly likely, they won't be leaving the EU simply if the UK pulled out anyway) the UK would effectively have to set up checkpoints on all public roads where the border goes across it. Otherwise it doesn't take a genius to realise that a major back door would be left open by such "undesirable" immigrants from certain EU countries simply landing in say Dublin, take a trip up north and either remain in Northern Ireland or catch a flight or boat across to Britain; travelling by air might be a bit harder as normally you're asked for some form of photo ID, but the ferry to say Stranraer or Liverpool would be piss easy to do, buy your ticket and on you go!
Therefore to properly enforce what they propose, they would have to break with nearly a century's relatively hassle-free cross border travel to the chagrin of the Irish government (who would have no desire to see such happen at least to Northern Ireland), almost all northern nationalists (should be too hard to see why they would be pissed off) not to mention a good amount of unionists whom would regularly go cross-border for business and/or pleasure (extra inconvenience if nothing else), with a consequential impact on the economy of border areas on both sides, one which the Troubles on its own caused significant hardship.
The problem of private properties that straddle the border with each part being in both countries would also pose additional headaches - take a lane up to a bit of farmer's land on the southern end, cross the border over private land and take a different lane off the farm in Northern Ireland. There's quite a few about, not to mention places like the village of Pettigo which straddles the border with one part in Co. Fermanagh (NI) and another in Co. Donegal (RoI) with the international border running across the middle of its main street.
The Labour party understands this. The Conservatives understand this. The Lib Dems understand all of the above. With UKIP what you have are policies that are written on the back of a packet of fags.