Where exactly is "Smitherines?"?

Actually, it's "smithereens".

Smithereens is an Irish word. It derives from, or is possibly the source of, the modern Irish 'smidirín', which means 'small fragments'.

Another enticing notion as to the source of smithereens is that it refers to the shards of metal formed when iron is forged and hammered in a smithy.

The notion of things being 'broken/smashed/blown to smithereens' dates from at least the turn of the 19th century. Francis Plowden, in The History of Ireland, 1801, records a threat made against a Mr. Pounden by a group of Orangemen:

"If you don't be off directly, by the ghost of William, our deliverer, and by the orange we wear, we will break your carriage in smithereens, and hough your cattle and burn your house."

"smithereens" is always plural.

The idiom is "smithereens". The most likely etymology is the Irish word "smiodar", meaning "fragment", and the diminutive -een (seen also in "colleen", a country girl).

"Smithereens" means little bits.