Who could this have been?
When you wake up and think you see something which magically disappears that is a dream. Kids cannot see things that other people can't but they do have more trouble telling dreams and imagination from reality.
It could easily have been a hypnagogic hallucination as they both occurred very close to waking during a period when your mind is just starting to wake up, and parts of it are still possibly dreaming. I personally wouldn't count or trust anything that happens (or seems to happen) during this time. I have lost count of how many times I've woken up in a panic to hearing knocks at the door. It's most likely your brain merging dreams with reality at this point. The fact that both events happened so close to each other is another clue.
What you are seeing is a spirit entity. It is not human, it may resemble someone in your life but in reality, it is not your family's ghost you are seeing. This is a demon. Demons are invisible but this one had manifested itself to you so it can lure you in. Beware --- demons are real, although invisible they are very hostile creatures and highly lethal beings. Demons are vicious creatures, they may appear to resemble your family but they are deceptive and can harm you. Many people gets in touch with spirits through using the Ouija board to contact dead loved ones, but only end up getting harmed by the wicked spirits. You seemed disturbed and bothered that this entity had appeared in your old home, and it resembles your mother's grandmother. My advice to you is: Do not over think on this. That entity was only posing as your great grandmother, and you getting into it could harm you. Occult is very dangerous. Do not allow yourself to be tempted to explore it. This entity, like I had said before, is pretending to be your loved ones, so that it can entice you to make contact with it ---- but it has nothing good for you in return. Wicked spirits likes to enslave people and use them for wickedness. Do not let yourself be enticed in anyway. Rebuke wicked spirits in Jesus' name, and tell it to go away next time you see it. "Go away Satan". This way they (the entities) will never bother you again. Here are some helpful bible based articles you can read to help you understand the situation much better. https://www.jw.org/en/publications/books/spirits-of-the-dead/demons-are-killers/#?insight[search_id]=3930d973-7645-4965-b423-ba4aa7b92b5b&insight[search_result_index]=1 Pray to Jehovah the Almighty God (Psalms 83:18) for His protection so that demons will not harass you again. Do not be afraid to pray aloud. Dangerous as they are, demons have limits, they are not as powerful as Jehovah God nor are they as powerful as God's son Jesus Christ.
Christian in Jesus
Yes, it was a ghost. They come to cause accidents to children. Your mother's essence kept it off of you. That is your mom's dna that the dark spirit was absorbing. They take good fortune from the living. You probably can remember some negativity about that time of your life. It is what sleep paralysis is about. Your mom probably befriended someone, not knowing they were from the shadow world.
Follow Aryatara´s advice.
Kids seem to see a lot more than adults can. I saw all kinds of things as a child. Not just humans but animals as well as mythical things but it all faded once I reached about six years old. EDIT! You really should take notice of Raro. Most think she is just guessing but she really knows little girls inside out. Wink wink if you know what I mean.
What about your great grandmother, your mother's mother's mother? Yes you might have seen a ghost or spirit. I have not seen a ghost, but I do sense them. They are my guardian angels, and they are from both sides of my family. All my family traditions die with me.