In Tennessee can a simple possesion & paraphernalia charge be dropped if my Miranda rights weren't read to me?

Generally, if you are under interrogation (and there are legal tests for this that even a first year criminal attorney will be able to help determine) and have been arrested, then you have your Miranda rights read to you.  Here, it doesn't sound like that happened.  Did they arrest you?

If the events occurred in such a way that led to your arrest, and your Miranda rights were not read (i.e., you didn't simply receive a ticket), then under the fruit of the poisonous tree doctrine, any evidence recovered could be suppressed (i.e., thrown out) absent any exceptions.  Plain sight is one such exception but how and why did they get invited in and what led them to your house in the first place.  The answer to those questions will determine if you will have luck having the evidence suppressed.

Although I generally agree with  my colleague's advice, I'd like to offer a few points to clarify.  First, failing to have your miranda rights read to you IS NOT an independent basis to have the charges dismissed.  It only becomes relevant when there is evidence that may be subject to suppression.  Second, the fourth amendment to the united states constitution prohibits searches without a warrant.  As my colleague points out, plain sight is a potential exception to the warrant requirement.  However, a bigger exception is consent, which, according to the facts that you have provided, your father gave.  I suggest that you consult with a criminal defense attorney to begin discussing this matter in greater detail and developing a strategy to defend these charges.  Good luck.