Thats what I couldn't understand when I started doing my family tree and found that he was adopted. I suddenly realised I couldn't trace anything about Theodore, to then realise that he was actually adopted. But like you say Frances, the family (James and Charlotte) already had 2 children, it didn't seem like it was planned (to me anyway).
Although I don't live there, my grandmother grew-up in Lancashire, as did my father. So although James and Charlotte Holroyd are from Yorkshire are relocated to IOM and Richard and Charlotte from Liverpool relocated to IOM, I wander if James and Richard have a link.
Also the fact that Theodore was born in Liverpool, where Richard and Charlotte once lived (not sure where the eldest sons lived Richard B Holroyd b. 1868 and Arthur Holroyd b. 1870) - may be they have a connection with Liverpool in 1901 and could be Theodore's father.
None of my family actually know that Theodore was adopted, I have literally found this out over the last few days. Sadly my grandmother passed away in 1997 and my father, I don't think has any photos. I may have some (I am a photographer and often beg for photos!). So I will do some digging around.