My father passed away several years ago, before I married and had children. Maybe the answer is obvious, but I wonder, does he know my children? Are our ancestors aware of the living?
I’m sorry for your father’s passing, especially that he wasn’t able to be there for your sealing and to spend time in mortality with his grandchildren. I’m sure that when he does finally meet them, it will be all the sweeter for him and them.
Regarding your question, I know of one teaching by Joseph Smith which seems to answer this directly:
When men are prepared, they are better off to go hence. Brother Adams has gone to open up a more effectual door for the dead. The spirits of the just are exalted to a greater and more glorious work; hence they are blessed in their departure to the world of spirits. Enveloped in flaming fire, they are not far from us, and know and understand our thoughts, feelings, and motions, and are often pained therewith.
Teachings of the Prophet Joseph Smith, Section Six 1843-44 Pg.325
No doubt you have heard stories about people being visited by family members who have passed on to the spirit world. While such events may not be common, and while those who have passed on are certain to have their own work to do in the spirit world, it seems that such events are common enough that there’s reason to believe the spirits of our ancestors are indeed aware of us. The following story was particularly touching to me. In it, a man tells of doing sealing work for his father who died before being baptized:
When we were in the sealing room to have him sealed to his parents, a warm glow came over me as we knelt around the altar. I knew my father was there in spirit. Looking at the temple president, I saw tears in his eyes. “Brother Snelson,” he said, “tell me about your father.” I started to tell him of the love and closeness I felt for him, but he interrupted me: “No, no—what did he look like?” As I described father, a gentle smile came across the temple president’s face.
After completing the sealing, he asked everyone but me to step out of the room for a moment. Taking me by the hand, he led me to the side of the room and we sat down next to each other. By then both of us had tears in our eyes, and the room felt as if it were filled with electricity. The temple president asked, “You know, don’t you?” “Yes,” I replied quietly.
He continued, “Your father was standing right behind you.”
“Through the Veil“, September 1983 Liahona
Whatever else your father may be doing, I believe he is aware of his family, including his grandchildren, and may even be very near them at times, as Joseph Smith said.