I'm getting sense from "Therefore I got a little furious and told her that either she'll sit there or we will rearrange the desks completely - at which she told me that I'm rude" that she heard some angry demands and responded with angry demands. Essentially, she fought fire with fire, and now you're both burnt.
My general rule is if I tell someone to do something, they get the right to tell me to go fly a kite with a hole in it. If I ask them how we can work together to fix the problem, they are obligated by norms of professionalism to attempt to find a solution.
Given that she has significantly more life experience than you, you might want to change your language a bit when working with her. Instead speaking to fairness, tell her why the arrangement of the dark corner with the back to door makes you uncomfortable. Ask her if she'd be willing to brainstorm a solution that will allow her to have some sunlight while allowing you to have peace of mind and enough working light. She may already have a solution in mind, but is holding back due to a burnt ego - if you approach her with a certain level of respect, she may relent.
If there's no solution to this, you might have to work your way up the chain of command. Honestly, if the office space really won't work for two people, they shouldn't put two people in there. If the space demands that one desk must always be shrouded in darkness, it doesn't sound like an acceptable two-person workspace to me.
All this being said, I'd like to point out that, while I'm sure there may be a possibility that you'll be corner for 20 years as you suggest, I'd say that possibility is small. People leave jobs (or get promoted!) all the time. Offices expand and contract. Buildings get built, torn down, rearranged, bought and sold all the time. Open offices become a thing. Remote working becomes a thing. Someone could decide to move across the country for reasons completely beyond your control. YOU could decide to move across the country for reasons completely within your control.
My point is: try not to treat this as such a big deal - the arrangement may only end up lasting a year or so, and if you insist on having an angry fallout over it, you will have wasted a lot of professional capital just to cause her to dig her heels in as hard as she could.