Coal miners did tend to move around different coal mines for work as one was depleted and others were sunk/expanded . Mine certainly did.
The best match that I can fine on the 1881 is
2 Front Street, Kilwinning, Ayrshire
Robert Montgomery, 58, coal miner, b. Irvine
Jane, 55, b. Stevenston
Robert, 21, coal miner, b. Kilwinning
Hamilton, 18, coal miner, b. Kilwinning
Agnes, 13, b. Kilwinning
And this from the IGI:
Birth, Kilwinning. - Robert Montgomerie, 2 May 1860.
Parents - Robert Montgomerie and Jane Baillie
Haven't got a firm hit on Jessie Davidson on the early censuses yet but there is a birth entry on SP in 1888, Shotts.
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