Well first off, most folks here will tell you to quarentine new birds for a time before just putting them in with yours. You never know what sickness, pest, or disease you may bring in.
Second, all flocks establish a pecking order. It's not pretty or "nice" but is non negotiable for your chickens. To us humans it looks like unkindness or someone bullying or being "mean", but the reality is that a chicken community will have order. Someone is always on top, and someone will always be on the bottom. In this case your home girl is letting the new comers know that she is on top.
Space is a big necessity, as long as you have enough room, roosting space, extra feeding stations and things to keep everyone occupied, with time everyone will settle into their places. Chickens are flock animals and do better together.
I recomend getting them out from the ducks and back with the chickens.
A little pecking is to be expected.
Good luck!