If you're comfortable, then you're dressing right. Mum's being Mum, and she doesn't realize how you warm up on the bike. Plus, 1.5 mi. isn't going to leave you out for very long. One idea might be to get a light nylon shell jacket to wear as a top layer, to keep the wind out and let Mum see you've got layers on, then you can stuff it in the backpack later. I wonder too if you might be better with a light wool sweater, which will breathe moisture out and stay warm,versus the hoodie,which I suppose is cotton and holds moisture. That's all I can think of right now.