How to approach my boss about not wanting the increased responsibility for a role that my company wants to cross train me in? Having actual nightmares about this.

I don't know how to bring up to my boss how much I don't want the responsibility they are trying to put on me (not even getting a raise). My current role doesn't have any role or responsibilities that can't be fixed the next day or week is something goes wrong. I am also not in charge of anyone.

They want me to take over the logistics role in our company so that the logistics person can take over another role (the person in that role was recently diagnosed with cancer and will be leaving).

It is work that could cost of thousands if I mess up when filling out customs stuff when we ship things (we move 2-3 containers a week from the US and South America).

I will have to start coordinating with dozens of people. Brokers, shippers, manufacturing plants, and customers (businesses not individual people)

AND I would be in charge of our driver. I would have to tell him when and where to pick up containers. I would have to call him for updates. If he does something that is violating whatever rules rig drivers have to follow, I will have to talk with him about it (maybe reprimand him?). I'll also be in charge of contacting Ryder if something goes wrong with the truck (I think we have a contract with him).

To top it all off, the person teaching me is TERRIBLE at teaching. She doesn't know why she does a lot of stuff, she is horribly disorganized (the two filing cabinets she has are a mess), and she just vaguely shows me how to do things at random. I have learned how to do a few things that just require data entry (the ISF for incoming shipment and paperwork for our shipments to the South American plants). It feels like I learned how to do those in spite of her.

How do I approach my boss about this? I am currently working part time because of Covid.

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