Well family counseling would be a good idea, but I imagine that one or both of them would not go.

If it is impossible to have a civil discussion with your grandmother, then don't try to have one. So for example:

Good job telling your grandmother not to speak in that manner! And you did that on your own. But must an argument ensue? Remember that it takes two people to argue.

You can still stand your ground and say that she is hurtful and ask her not to speak to you in that manner. In other words, just because she says "You're too sensitive" doesn't make it so, and does not "win" the discussion. You could even say something like "Insulting me might be a way to excuse yourself for speaking disrespectfully to me." Or you can, as I said above, end the discussion.

When you go to your mother it is called "triangulating" by family therapists. You might want to google that term. By going to your mother you imply that you are not in a position to handle the situation on your own. My thought is that at 25 years of age you are in a position to handle the situation without involving your mother. If your grandmother won't be civil and respectful you can minimize the amount that you engage with her, and you can say why.

Good job speaking to her! You can do this.

If she gives you the silent treatment, so be it. Do not make concessions so as to end the silent treatment.

I suspect that you want her to actually validate you. This desire, though, would put you in her power, as she could extend or withhold validation to suit herself and thereby manipulate you. It is indeed helpful to have validation from family members, but remember: you are valid whether or not she says so.

My advice is to deal with her yourself, without calling upon your mother to intervene. By that I mean speak your mind to her in a civil manner but do not get into an argument.

With regard to saying good morning and good night to her: My opinion is that you should just do that and not worry about whether or not she replies. Good morning and good night are small civilities and you can be the bigger person if she won't say them. I suggest that for you, not for her or for your mother: Being the bigger person is good for you, whether or not your grandmother responds.