As you say, it is a common name and there are a lot of Margaret Barrys
Is it possible that the Margaret Barry that married George Dodson in Petersfield was a Margaret Barrey born in Portsmouth,Hampshire in 1878 rather than the Margaret Barry born in the Lewes reg district.
Her birth was registered as Margaret Louise Barrey in Portsea in the last quarter of 1878.
She appears on the 1881 as Margaret L Barrey born 1879 in Portsmouth and living in Portsea. She was the daughter of George and Emily Barrey In the 1891 census she is recorded as Margaret Barry still living in Portsea with her family. I think that in 1901 she was recorded as Margaret Barry, living and working as a cook in Paddington
In the 1911 Census, a Margaret Dodson, born 1879 in Portsmouth is living in Binsted, Hampshire. She is with her husband George Dodson, and children Alfred (6) Violet(3) and Gertrude(4 months).
One factor against this identification is that the couple say they have been married 9 years but I can't find another marriage of a George Dodson that would fit.