Oh so your family were in the border districts. They had no way of knowing which side of the border their lands would remain after Partition, or maybe they were too sanguine they would be part of Pakistan. Many people weren't sure that a Partition would even occur because the proposal for an actual Pakistan was accepted very late. Even until mid 1947, there were plenty of backers of a unified India. It was felt by them that Muslim League proposal for a Pakistan would eventually be defeated. Everyone basically underestimated Mr. Jinnah, but he was very resolute in his demands. And here we are, you have your own country!
Mahatma Gandhi made one of the historical blunders of his life by not stepping out of the scene; all the fasting he did made matters worse (later Nehru pleaded with him to step out of the scene and let him handle it.) He wanted a unified India even though it was no longer a possibility. Gandhi's idealism wasted many crucial months and possibly years, that would have given the families enough time to transfer smoothly. That's why it's not always beneficial to have good people in charge of a crisis. What you need is brinkmanship and level-headed practicality.
However, no one was expecting communal riots on that scale. It was really spontaneous. And as I said, the lack of policing and poor infrastructure/communication in 1947 meant the situation could not be controlled well.
Nehru did not get along that well with Jinnah on a personal level. Had there been more camaraderie between the two, maybe the transfer would have been smoother.
But the real villain of the haphazard Partition were the British authorities in charge. They were apathetic to any potential genocides ("let the brown people kill each other, who cares?"). Cyril Radcliffe only arrived in India on 8 July, 1947. Before his appointment, he had never visited India and knew no one in the country. The British thought that because he was so ignorant, he will be more neutral. But he really behaved like Donald Trump did during the current US Coronavirus crisis. He did not do any field surveys: in fact, the entire Radcliffe line was drawn in just a few hours during afternoon tea. And both Congress and Muslim League representatives were given exactly two hours to study it. After that, Radcliffe submitted his proposal without consulting anyone. And that was on August 9, 1947. He knew there would be a backlash later so he quickly burned all his research papers, and immediately departed India on August 15 itself.
Also, Mountbatten was more sympathetic to Congress cause. Nehru was on very friendly terms with him and his wife, Edwina (many BJP idiots argue that they had an affair but they were just good friends, nothing more. That miserable wretch, Narendra Modi, cannot attract
even an ugly woman like this one.). In all fairness, Nehru tried his best to win more territories for the Congress just as Jinnah did for Pakistan. Nehru even wanted Lahore, but Jinnah wrested it away from him. It was really a chess match. There should have been more give and take on behalf of both parties. But Nehru was definitely a strong negotiator on behalf of the Indians. Also he was very patient and could play the long game. Against all odds, he waited until the end of 1948 to resolve Hyderabad and up to 1950 to resolve the Indian side of Kashmir. He waited until 1961 before the Indians could annex Goa from the Portuguese (first time in that slice of history when brown people fought against white people, and won without any contest!).
In hindsight, I think Nehru was too good for today's Indians. Given the current custodians of the country are illiterate mini fascists, they have benefited from the best leader we ever had. They are not worthy of the legacy he created, the India he had built through patience and hard work. Today's generation of Indians should be really getting down on their hands and knees and worship Nehru for his immense and sole contribution in building this nation. But instead his legacy is being befouled by the ingrates affiliated to the BJP/RSS.
Lastly I must say that the human toll of the tragedy was too much. While Pandit Nehru is my role model (I mainly salute the amazing work he did for independent India and its economy), his decisions have definitely caused disturbance in the lives of so many Muslims (although it has benefited many more people). I would like to apologize on his behalf to you, and families like yours. I am also in favour of someone from current Gandhi family apologizing to the Muslims uprooted from India. But maybe it will never happen because of obvious politics.