Have you traced the witnesses to the 1906 marriage? Are there any possible clues there, or are they clearly on the Dawson side? How was Gertrude's father described (exactly) and what was her address at marriage?
John Robins is described as simply as 'Merchant." One of the witnesses was a Frederic Robins. John Robins (the Hat and Cap manufacturer) had a younger brother called Frederic. (same spelling without a k) In that same year, around the same time, Frederic, who was married the year before had his first child and named her Blanche
Gertrude Reardon Robins. Frederic gave all of his children the middle name of Reardon because that was the maiden name of his mother. Census records show that their mother was born in Southwark, London. But Reardon is a distinctly Irish name, and her parents may well have been Irish, which may account for the Irish references. For me, this is fairly compelling evidence linking the schoolmistress to the actress, but by no means conclusive. Doubts persist. But if these two women are not the same person there are some incredible coincidences at play.
Gertrude Robins, (the assistant schoolmistress, at least) is my first cousin twice removed.