Overly aggressive kitten

I live alone with my 5 month old kitten. However, whenever I am on semester or holiday break from school, I bring her home with me, where there are 3 adult cats. They will hiss and spit at each other, and then leave each other alone. However, my kitty will stalk and run after the big kitties like she wants to play and then gets up close to them, spits and swats. She hisses and swats my mom when she walks by and even hisses and swats me when I touch her. Shes constantly walking around grumbling and growling, even if no one is pestering her. I dont know if this is a game that kitty is playing but its causing some problems with my other cats. I know that introducing a new kitty into a house takes time, but this other behavior seems abnormal to me. What can I do to intervene and stop it?
Also, does acepromizine (sedative) cause cats to become aggressive? When she flies with me she gets .2 milligrams for each flight and a few hours after the sedative is given is when she is most noticibly nasty to the other cats, my family and I.
Thank you for any advice

I think a lot of it has to do with her being a kitten. Her instinct is to try and play, but when she gets close the other kitties she smells then and then her instict tells her to be defensive.

It also probably doesn't help that most of the time she is not around these cats so each time she visits, she has to be reintroduced. And she probably feels threatened by the fact that there are three of the other cats that know each other and live together and just one of her.

I don't think she is overly agressive, I just think that being in the situation and being outnumbered causes her to feel defensive.