Is a gelding a better choice to buy rather than a mare, Why?

I have an Arabian mare, she is a pain in the ! She is well trained and everything, and I ride her every day. I prefer and so does she but recently I was clipping her and I had finished and started to untie her and she rared before I finished untying her and my thumb was in between the board and the lead rope and it skinned and sprained my thumb. She also has rared up and flipped over on top of me and the ambulance came and raced me to the hospital because I couldn't move but I was in shock. I know she wouldn't hurt me on purpose but she does have an attitude. I have raised her since she was born. Her mother died from being chased by some stupid hound dogs and she slipped in the mud and broke her hip. There was nothing we could do. My horse was chased by the dogs later when she was 3 and tried to jump a barb wire fence and it cut open her chest. We stitched it up and kept her in a clean stall until it healed. She was exercised every day but nothing more than a walk around a large hay field. She has an attitude that I dislike very much and I need another horse for my dad and friends to go riding with me. But I want a calmer horse than her and doesn't have her temperament every 28 days or so. I would like to get a quarter horse by the way and I want to be in the rodeo but im afraid to do anything public with my mare because of how rude she is to me and embarring she is around others with their horses. Thank you to all who answer my Q. All answers will be put into mind when we look for the right one! Please answer ASAP. Thank you