C.G.
You are very wise for recognizing the need to correct this behavior now. As others have said, you do not want her to grow up thinking it's ok to disrespect others, especially adults.
Ahead of time, you could have a talk with your husband about what's about to change and let him put in some of his own ideas so he is involved. Next, the two of you could talk to "Pa" to tell him about a family meeting and what it's going to be about. Let him know that you all feel very blessed that he is able to live there and spend this time with his grand children. Tell him that you want to raise your daughter to be respectful, but the way things are going right now, this is not happening. He may be feeling like since he is not the parent, he isn't qualified to discipline her. He may feel like he's stepping on your toes if he tries to enforce some rules. You could let him know that everyone in the house is expected to respectfully enforce the rules from now on in order to have consistency. Also tell him that she will still love him even if he enforces the rules. They could actually begin to have an even better relationship when there is mutual respect between them.
Next, involve both your daughters and have a meeting where you all decide on the house rules together. Your daughters can be helpful at this and this will help your younger daughter have some ownership to the rules. Keep them simple and only make rules about what is important. Some can be general like "Respect each other" so that this covers name calling, ignoring, talking back, etc. Then, talk about what respecting others looks like so that your younger daughter has a full understanding. A little role playing and acting out scenes could be a fun and effective way to do this. Some rules may need to be more specific.
Let your family know what the consequences are ahead of time. Your daughters may be involved in this too, with your guidance. When your daughter misbehaves or breaks one of the rules, make sure everyone knows how to follow up with the consequences. Logical consequences work best. If your daughter throws a fit because she can't have something, have her sit in her room or do something quietly until she is ready to use her words and act appropriately. She can decide when she is ready. This is more effective than taking something away, as taking something away is totally unrelated. If they can make a connection between the behavior and the consequence, it's more effective.
Remember that children don't automatically know everything from birth. We often expect children to know how to behave when no one has ever really taught them. So far, no one has really taught your daughter what kind of behavior is acceptable and what is not. So, look at this as a learning experience for her. Think of what she needs to help her LEARN when you are thinking of rules and discipline. It will probably take more than just rules and consequences. When she misbehaves, follow through with the consequence, then get down on her level, eye to eye, and talk about why her behavior is not ok in terms she can understand. Make sure your tone of voice is firm, but still respectful. For example, you could firmly say, "That really makes me sad when you...and it is not acceptable. Next time when you are angry, instead of ...., you can use your words to tell me/talk to me in your big girl voice/etc." In helping her learn, it is important to focus on what she CAN do next time, rather than what she can't do. This will help her learn new, alternative behaviors.
Also, in general, I have found huge improvements in behavior when I focus on all the positive things kids do rather than the negative. Spend more time verbally praising her, being silly with her, and just having fun together. Then, it can take some of the focus off of always disciplining her. Also, when kids are constantly being disciplined, it kind of all starts to sound the same to them if they are always being corrected and they don't really "hear you" anymore. They stop paying attention. If you make a bigger contrast between playing happily and then disciplining, they are more likely to pay attention when you are firm with them. I'm not saying to let things slide, just make a bigger contrast between happy times and discipline, instead of constant discipline.
Sorry this is so long, but I wanted to give you some specific example of how to follow through with this. I work with young children and have tried lots of different ways of handling discipline. Something different works with each child, but these ideas generally work.