Robert being 20 yrs older would be no impediment in itself (I was looking at a family yesterday, same age gap and the wife managed to have 13 between ages 20 and 39!) - however, if there were no children to the marriage in 1911, being 3 to 4 years after they married and if the 1911 census didn't indicate there were any children born to the marriage (living or dead), then I'd be somewhat surprised if there were any at all. Maybe the 1912 birth, but unlikely not 1930, 1930 or 1934? Never say "not" of course, unless proven but....
We do know from Robert's Probate in 1948, that Fanny outlived him:
Robert ROBINSON of 9 Cross Street, Eccles died on 19 February 1948.
Probate was issued 25 March 1948 Manchester to Fanny ROBINSON, widow.
Effects: £1838, 9d, 6p
Have you discounted this:
DEATH: Fanny ROBINSON, age 77 (born abt 1885), registered Barton Mar Qtr 1962
As for the child, Robert Jnr. If he survived his birth and infancy, have you already checked to see if he is with any of his mother's family?
Cheers
AMBLY