I have some bits and pieces that might help.
It looks to me that the Hugh Shimmin b 1820 is the son of John Shimmin and Elizabeth Shimmin md 26 Aug 1809 Braddan. The IGI has some children of this couple that match the dates in your note. So we have Shimmin marrying Shimmin.

You're right about the elder Hugh Shimmin, and his two marriages. His first son of his second marriage, Philip Shimmin bp 1801 Onchan married Isabella Gelling in 1827. Isabella is most likely the daughter of John Gelling and Isabella Cavendish. The Shimmins were from Ballaugh. The Gellings are my connection to this, though I'm not related to these particular people.

There is a John Shimmin bp 1789 Braddan, son of Hugh Shimmin & Esther Lewin, which is Hugh's first marriage. The only Elizabeth from this marriage died and there doesn't seem to be another one. So, the family connection looks pretty good though not proven.

I can't determine the connection to your Annie Ellison though as being a "niece" of Hugh Shimmin, which I think is your main question. What else do you have for Annie?