I've been following this and doing some research and it's confusing to say the least.
1. Randolph Parsons seems to have spent all his life in Birmingham - in 1939 he's still shown as married (and there's not been another marriage for him) so no divorce I would say.
2. You say your fathers' sister was Alice Maude born 23/1/1922 Droitwich - this birth is in the name of Parsons, mothers maiden name Parsons suggesting an illegitimate birth to a single lady named Parsons. You go on to say on your other thread that Alice married as Alice Gough to John Randell in 1937 BUT this can't be right, surely, as she would only have been 15!!
3. Your fathers birth is registered as Parsons, showing mmn as Taylor (and you say her name is given as Mary) but with no fathers name. This itself would thus indicate that a Mary Taylor had married a Parsons and although still married her husband wasn't the father of her child (her legal surname would still have been Parsons hence child being registered as Parsons).
As was asked earlier how did you make a 'link' that Mary Parsons, nee Taylor was actually Mary Parsons, nee Hodgkins, wife of Randolph??
Where was Mary in 1939? When/where and under what name did she die?
Annette