So we're looking at the United Arab Emirates and the borders it shares with Oman here (Oman to the SSE and NNE). Just off of the East coast to the NNW of Fujairah you can see that fun border. That's Madha.
Madha is an Omani exclave in the UAE. Exclaves aren't too uncommon but: Nahwa, the second-order enclave inside of it, is. There are currently only two places in the world with second-order enclaves: Madha and an absolute mess of an area in the Netherlands/Belgium.
The roads are connected and the borders are soft so it's not the biggest issue in the world. But if you were an Omani from down the coast in, say, Sohar to the SSE, to visit Nahwa Cave you would have to cross the border into the UAE, cross the border into Oman, then cross the border into the UAE. Fun!
Why did this happen? Basically, the leaders of 4 rival clans (that included an Omani clan and the clans that represented 3 different UAE emirates) gathered folks from Madha in late 1930's/early 1940's and asked them to pledge allegiance to one of them. The Madha people pledged allegiance to the Omani clan, but people from Nahwa chose to stay loyal to the Sharjah clan (a part of the modern day UAE). Later on when the ol' colonizing tea drinkers controlled the territories (1969), the borders were officially established. Woo!
And here's that Nahwa Cave! (source)