I think there might be two Catherine Spowarts. Which is what is causing the confusion, or adding just to the uncertainty.
There are shipping entries for I think Walter and his son Robert going over to the US, together in 1868:
Walter Beveridge, 45, miner and Robert Beveridge, miner, aged 22 both b. Scotland. Arrived NY on the 'Caledonia' on 3 Aug 1868. Departure port Glasgow.
There is also a further entry for a Walter Beveridge, miner, also arriving in NY on 15 Jun 1869 also aged 45. Departure port Glasgow.
Toddler Walter, son of Isabella and Robert, also shows as travelling with mother Isabella, arriving into NY on the 'Iowa', from Glasgow on 13 Jul 1869. Departure port Glasgow.
By 1885, Walter Snr., widowed and aged 61, sonns Robert and his family, James and his family are all showing as living side by side, the men miners by occupation in Marcy, Boone, Iowa.
Lynn, the second marriage for Walter that you mentioned shows here
https://familysearch.org/pal:/MM9.1.1/XJC9-LTHMonica