I like your analogy, iloveds.
Anyways,... is there a difference between mind and Dharma?
Personally, I feel that the Dharma is learnt to tame the ever wild mind of ours, and therefore, if we just learn Dharma as an intellectual subject and not put it into practise through our minds, then it is of no use at all. If we learn something and not put into practise what we learn, then what is the point of learning it in the first place? It is like separating education and knowledge from application. Then everybody doesn't need to go to school/university, no? If what we learn, we cannot or do not apply, does it not show that ultimately it does not work? It further increases ignorance, because you act and live as if you would know everything.
So then, if the mind and the Dharma is separate, then what we end up doing is directly going against the Dharma, because we let our minds attach further into the complexities and attachments of life. The Dharma is learnt to be applied, for us to cut ourselves from further diving deeper into samsara, for us to develop the qualities to bring us a step closer to enlightenment, and for us to relieve ourselves from suffering. If you know what you are doing is wrong through understanding/learning the Dharma, then not mentally applying, which is reflected through your actions and speech, contradicts your knowledge. The actions of the body, speech and mind are all inter-connected, and that comes from the application of knowledge and wisdom.
Dharma and your mind has to be one, because you are a reflection of yourself - your mind, your knowledge, your understanding. Everything comes from the mind.