Help us convince my mom!

Okay so...my younger sister and I want to take a road trip this summer back to where we used to live so we can see our old friends and also some family that live there. I'm 22 and have a one year old who will be coming with and my sister is 17. We both still live at home, myself for complicated reasons. The trip will be a total of about 20-22 hours. I have done this trip myself alone about 4 times and we've also done it with my son once as a family. We plan to make tons of stops for baby to get out and stretch and we have literally everything planned out including where we will stay overnight along the way. But my mom is still saying no to my sister coming. I won't go without her and it's more of a bonding thing with us before she goes off to college. Any ideas we could use to help convince my mom? We don't understand what the big deal is. We're both very responsible and don't get into any trouble and she knows who were staying with and who we will be seeing. TIA