I don't think the list of tasks will help - though I see why it was suggested.
The problem is that they are making this into a two way conversation, which it shouldn't be as it is YOUR decision. By opening up the "if the filly stays, you will have to do this..." line, you are acknowledging that there is a possibility that the filly COULD stay. Which is the opposite of what you are wanting to achieve.
I say you wait until you are ready to move her, and then phone and say you are coming up today to get her. Buy your mum a box of chocolates and a teddy bear to let her know that you appreciate that she had done a good job, and that she'll miss her.
I suspect that the real problem here is the friend who doesn't want her gelding to lose his field mate. He may have a real problem with being alone. It is courteous to the geldings owner to let her know that the filly is going as she may need to make alternative arrangements for a companion. Can you phone her direct?
Finally.....we all regress to childhood when dealing with our parents! Just imagine that this is a barn owner with whom you have a friendly and respectful arrangement. Be the adult you would be with her instead of the child you are being with your mum.