Wow - I'm impressed. The Yorkshire dialect in the Secret Garden must be very difficult for a non-native speaker.
First, to translate from dialect into standard English, this would be "He knows we daren't call our souls our own" (or "He knows we don't dare to call our souls our own").
I assume you understand the individual words and it's the phrase you are asking about. It isn't a standard English phrase and I would say a lot of native speakers would struggle to explain it - I do! However I think it refers back to Martha's fear that she will be sacked ("I shall lose my place...). Everyone has to do what Colin wants and Martha is scared of doing even the smallest thing to upset him - so she says he knows she doesn't dare to "call her soul her own" as an exaggerated, metaphorical way to say that Colin knows she feels she has no choice about obeying him (because she might be sacked if she upsets him). Obviously everyone should be able to say that their soul is their own, so the phrase is emphasising how unreasonable Colin is.
Hope that helps!