1881 Census: West Haven Farm Cottage, Panbride
James Kidd, 27, farm servant, born Arbirlot
Margaret Scott, Wife, 22, born Dundee
Mary Kidd, daughter 1, born Monifieth
John Kidd, brother, 29, general labourer, born St Vigeans
James Kidd, head, 28, agricultural labourer, born Barry
Elizabeth Raitt, wife, 40, born Panbride
Barbara Kidd, daughter, 10, born Barry
Jemmina Kidd, daughter, 8 born Panbride
James Kidd, son, 4, born Panbride
Elizabeth Kidd, daughter, 1, born Panbride
all listed in the LDS CD-ROM as one household. You'd need to look at the original to see if they are actually recorded as two separate households, as seems likely.
In Kinloch Street, Barry (i.e. Carnoustie) in 1881
John R Kydd, 69, retired salmon fisher, born Barry
Barbara Kydd, wife, 69, born Barry
I am a bit dubious about the age given for James Kidd. James Kidd and Elizabeth T Raitt were married in Panbride in 1868. If he was 28 in 1881, that means that he was only at most 16 when he married. It is almost unheard of for an agricultural labourer to marry at only 16.
So I couldn't resist a look at that 1868 marriage. Sure enough, it's James Kidd, aged 25, farm servant, son of John Rae Kydd, linen weaver and Barbara Mitchell. James was actually born on 5 February 1843, so he was 38, not 28, on the day of the 1881 census.
Anyway the point of all this is that John R Kydd, in Kinloch Street in 1881, is the father-in-law of Elizabeth Raitt or Kidd, and the grandfather of Barbara Kidd, who died in the fire at Souther(n)wood Place.
Kinloch Street is all enumerated in Enumeration Districts 2 and 4 in 1881. John R Kydd is in ED4. This ED includes Brown Street, Lower Kinloch Street, Burnside, Dundee Street, West Path and Braefoot (though not necessarily all of any of those streets), plus Agra Bank House, Carnoustie House and Lochead Farm.
John R Kydd's is almost the last household enumerated in a longish list of houses in Kinloch Street. There is just one household listed between his and Lower Kinloch Street, and there are no listings of households in Golf Street in Barry in 1881. So I think that this supports the idea that Southernwood Place must have been on the corner of Kinloch Street and Golf Street.
Noting that the article says that Barbara Kidd had let a two-storey house for August, and moved into a single-storey one, and that the cream-coloured two-storey house with attached single-storey cottage is older than late 19th century, I think the answer to your question is thst Southernwood Place is still there, but the name has been lost.
What isn't answered is what happened to the five other houses in Souther(n)wood Place listed as tenanted in the 1935 valuation roll. Looking at Google Streetmap, I see that just east of the cream two-storey house single-storey house is a terrace of single-storey late 20th century houses. I think you may find that these stand where the home of your Beattie family stood.
They might possibly have been in flats in the white building right on the corner of Golf Street, but the description of the tenanted dwellings as 'house and garden' suggests not.