Q: 2003 Mini Cooper struggling getting into reverse, unles going into third gear first

It’s pretty common with these Minis. You might have the shifter bushings checked. Maybe the bushings are starting to wear. But those Minis are not the greatest built vehicles. As they age, they get all kinds of problems. I would personally be careful with it if I were you, because as they get to age, things are going to break down and cost a lot of money. You don’t want to spend a lot of money on that car because they have a very poor re-sell value and are not worth much when they are 13 years old like that. If you want to have this issue addressed properly, have a technician, such as one from YourMechanic inspect your gear shifting issue and let you know exactly what needs repair.