Here is an old thread where we discussed the issue of dominance:
Behavior Poll.
IMO, a parrot wanting to shoulder and/or get on your head is simply an issue of them wanting to be up high where they feel safe. Most birds don't like to be down low- Ollie gets nervous when she is anywhere below knee level.
If you don't want her on your shoulder, just remove her. It'll take time and patience, but eventually I think she'll give up. I trust Ollie, so her being on my shoulder isn't a big deal at all. I'd rather her not be on my head for the reason that I can't tell when she's going to poop.
Maybe Dozy doesn't feel secure on your hand? Make sure you're very stable. Praise her when she's where you want her, and remove her quickly and consistently when she's somewhere you'd rather her not be.