OK, this is a bit confusing but I think we maybe getting close to what I am doing wrong.

Do I play the Dorian shape starting from those different starting points?

Because if I do I get the A minor from the A, ACE, as you say, but if I do the same with the C, I get C E flat G.

And now I come to think of it if I start at G I get an A sharp on the third degree, so I didn't get a G major after all.

thanks again