I'm going to leave my mother to go on a ski trip
Why would you leave your mom to go on a ski trip?
My mom is annoying when she stays with me for too long
Sometimes its good to take a break from someone you love. They will understand if you want to do other things without them.
My mom just doesn't know when to leave.
Sounds like you need to sit down and have a talk with your mom. Tell her you love her to visit, but that you have other obligations you need to deal with as well. By setting a timeframe for her visits, you'll be able to better organize your time together and  make the time you share more enjoyable.