How to convince my stubborn mom *short*?

So, my friend and I are 1 year apart. She's 13 and I'm 14. Her name is Mary. So Mary's mom works everyday as well as her dad, so they have to put her at her baby sitter. And I stay with my grandma at home. We could invite Mary over but my grandma is suffering from pneumonia and that can be very contagious. So Mary's mom suggested that I go to her place in the morning and me and Mary can stay home alone until 5 or so. I would go there at 9:00 or something. What's wrong with 2 friends staying in a house together? We know not to leave the house, but my mom is over protective and she won't let me go!!!! How to convince her?

Thank you to everyone who answered in advance :)