Linda
I don't think you are clutching at straws - I think you are right in what you are thinking. Likely he did leave his family sometime from 1906 - 09, at some point following the registration of daughter Barbara's death when you know he registered her death.
The why's will probably be hard for you to determine I'm sure. I don't think there was a divorce, wife Ann still showed as married at her death and Hugh showed as a 'widower' on his 1909 marriage in Newcastle.
The name Hugh Lovatt (and the number of variants), is relative rare in both Scotland and England. Lovatt by the way is the more Irish spelling of it which fits with father Hugh being Irish.
There are no deaths showing for Hugh in Scotland that I can see. To give you an idea of how rare the name is in Scotland, between 1855 to 2006, there are only 6 entries, of any age, in the whole of Scotland.
Of these 6 deaths:
1996 - Hugh and Annie's son, Age 0 in Falkirk
1904 - Hugh Snr I would imagine, age 67 in Larbert fitting that 1901 census entry we found
1935 - probably a newphew (?), age 37 in Larbert*
*I found another brother of Hugh's the other day . A Donald Livitt married Ann Jane McDade in Falkirk in 1898, son of Hugh and Margaret (McIver).
I do think you have found your grandfather's family. From what we have seen in the censuses and BMDs, it fits in great part what stories have been handed down through the family. You have his birth in India, his father in the army and his occupations showing on the censuses and certs.
You also have the use of family names he used for his new family, No.2 Hugh, Marion and Donald (who we now know was a brother of Hugh's).
Hugh stating he was a widower and referring to a criminal past may have been his way of keeping the door to his other life in Scotland firmly shut....
Monica