I note the marriage & children you mention.
DAVIDSON WILLIAM - WILLIAMS MARGARET ANN 1914 Dalziel
Children Registered Dalziel.
Child 1: William 1915
Child 2: Mary (Helen) Ellen 1916
Child 3: Robert Edward 1918
Child 4: John 1925
Child 5: Susannah 1924
From the list posted by Colin with a clear order. I think the birth entry you posted for a Margaret Ann William in 1887 is very likely the correct one.
James/William and Margaret Ann look to have followed naming pattern in respect of the names connected with her. I think her father was a Robert Edward Williams and mother Mary Ellen Plunkett. Likely marriage for them in Wrexham, England in the last qrt of 1878 (vol 11b/ p 482).
This looks to be the Williams in 1891
Robert Williams 34 coal miner b. Wales
Mary E Williams 28 b. England
Susannah Williams 11 b. Wales
Herbert Williams 10 b. Wales
Margt Ann Williams 3 b. Burntisland, Fifeshire
James Williams 1 b. Cowdenbeath, Fifeshire
Joseph Williams 1 Month b. Bellshill, Lanarkshire
Address: Main St, Bothwell, Lanarkshire
From Family Search, the 1881 census gives you the specific birth places in England and Wales
https://familysearch.org/ark:/61903/1:1:Q2WS-CDCD (you need to be signed in to view now).
An old post here on RC regarding Mary Ellen Plunkett
www.rootschat.com/forum/index.php?topic=555287.0Monica