Bec - I second what Fi said.... and Eliza is not a bad child. She is amazing, gorgeous and wonderful. Like you said, she likes her own space. At this age, our children are very egocentric and don't really "play" together in the classical sense. They can play alongside each other but kids don't generally play nicely together until well into Primary School age.
Like the others have said, she's just being assertive...whether it be at childcare or other places where there are lots of children.
Other parents are probably happy that you follow up on Eliza's behaviour and that you're not just brushing it off.... you're doing all you can (and you're doing a great job at that).