At present I have 4 kitties and 3 are afraid of the vacuum and one thinks it's a toy and tries to play with it when it comes out to play. In the past I've also had dogs that were also afraid of the vacuum. I don't think fear of the vacuum has any correlation to abuse. I think it's the sudden change from quiet to noise that bothers them. The broom could mean that someone shooed them away with it or sadly, it could mean someone hit them with it. Keep in mind that your kitty is new to your home and she needs time to adjust and establish her place in it. If you got her from a shelter than you're at least her third home. That's a lot of moving around for a kitty 2 years old. If she was born at the shelter then it's a lot of time to live in a cage.
New people are about the same. When someone knocks on my door they don't bother to wait to see who it is, they simply run and hide. If it's someone who comes in and visits two of them will eventually come out to see who it is but the other two will stay hidden until the visitor is gone.
What I do to help my friends is not force them. If I'm going to vacuum in one room I make sure the ones who are afraid are not in the room then close the door before turning on the vacuum. When someone comes to visit I don't try to make the kitties come out so they can be seen. If I want someone to see one of my kitties who is shy, I show them a photo.
Two of my kitties came from a shelter. One was a house pet (Mischief) who had been turned in and one (Little Boy) was turned in without an history. Mischief had been in the shelter for about 3 months but Little Boy had been there for 6 months. I've had him almost 7 years and he still won't let me pick him up but he'll sit in my lap, curl up next to me at night, and sometimes sit on my shoulder but if he thinks I'm about to pick him up he'll run away. Little Girl was starving and near death when she dragged herself up on to my patio one day and Little Bit was born to a teenage mother who abandoned her. She came to live with us when she was about two months old and instantly had 3 kitties who took turns taking care of her. She's the one who is fearless.
If you just love them and allow them time to adjust to new surroundings and people they'll be okay. Doesn't mean they'll ever love a vacuum or strangers, but they will love you...