Let's start by saying that you have asked a legal question. To be truly safe, you should really only rely on an answer that you receive from a lawyer that you have paid for advice.
That being said, federal law allows that, under certain conditions, you can transport your weapon between any two places where you can legally possess it. Since you have a Ma LTC, you are good at your starting end. I believe that in CT you do not need a permit to legally possess a weapon in your own home, so you might be good at your grandfather's end as well. Once again, I am not a lawyer, so you should not rely on my advice. Seek legal counsel.
jeff