I want to tell a customer that she needs to calm down
Why does she need to be calmed down?
I'm just having a stressful day and I would like to get home as soon as possible
I'm sorry your day has been bad, and it is also another part of your job to diffuse bad situations. You are doing a good job by wanting to calm her down, so no issues can escalate at your workplace.
It's not my fucking job to do that.
It sounds like you need to talk to someone in charge and bring up the situation to them. If you're uncomfortable diffusing these situations and it's not a part of your job then you shouldn't be expected to do so.