First of all, I'd like to say that I think it's wonderful thing you are doing...raising your granddaughter. And, also, be so aware of wanting her to have manners. It seems to me that so many parents these days don't see the importance of children knowing how to behave or be polite and I think it's a shame. I was "southern raised". We said Yes mam, No mam, Yes sir, no sir. We called people, unless they were relatives, by their last names, Mr./Mrs. Jones. If we were more familiar, we called women Miss Peggy (Or whatever her firt name was). My parents were not tyrants, by any means, but my sister and I were raised to act like little ladies. Oh, we climbed trees, went fishing/camping, rode bikes, got filthy dirty, but we still had to say please and thank you. Interrupting was a SERIOUS pet peeve for my parents. If we interrupted, somebody BETTER be bleeding. My dad taught us, from the time we were very little, that if they were on the phone or talking and we needed something, we could approach and gently tug on a sleeve. Two tugs. If they did not acknowledge us right away, we went back to what we were doing or went to another room, knowing full well that in a few minutes, they would either call for us or come to find out what we wanted or needed. We didn't stand and hover or tug, tug, tug. The tug was our silent signal and they never failed to let us have our time to say what it was we wanted to say. Somehow we just knew that if what we wanted was something like, "Can we play in the front yard instead of the backyard, or can we have some watermelon", we would live the 5 or 10 minutes until we got the answer. If someone was hurt or it was SUPER important, we would still
tug and say, "Excuse me for interrupting...."
I think it sounds like your granddaughter is wanting attention and to be part of the conversation. But you are right to let her know that interrupting to let you know the sun is out is not appropriate. It's not wrong for her to notice that, or even be happy about it. But when other people are talking is not the time to bring it up.
My friend's son, who is 11, was never an interrupter but started it all the sudden. "I found a rock outside. I had pancakes for breakfast". They invited people over and instead of playing with the kids, he was in the family room tumbling and rolling around the floor in front of everyone. Of course, he is a little older, but she just started calling him on it. In front of everyone. She would say, "People are talking and you are interrupting. You know that it's rude, and you are still doing it. Would you like to say you're sorry and go outside to play with the other kids, or would you like to go to your room alone while everyone is here?" He always chose to go play.
There is absolutely nothing wrong with engaging children in conversation. That is how they learn to converse.
Try practicing with you and your husband. Maybe have a trusted neighbor or friend come to visit and if she interrupts, call her on it. If someone asks her how her day is or what she had for lunch, let her say, and then ask her to excuse herself while you continue your visit. Like I said, my friend's kid thought everytime adults came over, it was "The Logan Show".
Just talk to your little girl. Let her know that you love her and talking to someone else does not mean you forget she's there. Everyone loves her and knows she's there. She does not need to interrupt. Try the tugging thing. It worked for me and my sister and our kids. She'll get settled in and I really wish you all the best of luck with her. My hat is off to you!