Mildred Hayes: I don't care if you never did shit or you never saw shit or you never heard shit. You joined the gang. You're culpable. And when a person is culpable to altar-boy-fucking, or any kinda boy-fucking, I know you guys didn't really narrow that down, then they kinda forfeit the right to come into my house and say anything about me, or my life, or my daughter, or my billboards. So, why don't you just finish your tea there, Father, and get the fuck outta my kitchen.
Mildred Hayes: Hey fuckhead!
Dixon: What?
Desk Sergeant: Don't say what, Dixon, when she comes in calling you a "fuckhead."
Mildred Hayes: This didn't put an end to shit, you fucking retard; this is just the fucking start. Why don't you put that on your Good Morning Missouri fucking wake up broadcast, bitch?
Answer: Since the movie doesn't tell us how she and Bill met, any answer about how and why she was there would be mere speculation. Letting an actress speak in her native accent is not exactly "random"; random would be if she was an American and the writer/director decided to make her character Australian. However, the situation of an Australian marrying someone from, and then living in, a small Missouri town is not as outlandish or nonsensical as one might think; I used to date someone from a tiny town in Kansas, whose mother was an upper-class British woman who happened to meet and marry someone from that town.