It's not stubbornness...it's one heckuva awkward position, pooing on a western toilet. We're just all used to it since we've been doing it for decades.
Just as an example: I DARE you to poo standing up or laying down. It can be done. Don't bend your legs, just lay flat, sideways, or stand up straight. This is essentially what we ask our kids to do, something COMPLETELY different from what we're well practiced in. And a LOT harder to do than peeing. Now...if you took me up on my dare, you'll have noticed something: you would have wanted to pull your knees up to your chest. The "squat" is natural. It's easy, fast, and comfortable. It's what babies, toddlers, and several billion adults in Asia do. You would NOT have made a right angle with your legs so that you looked like you were sitting on a chair. Even birthing...where do our legs get put when we're pushing? Like a gyn/ob exam? Or do they get pushed back? Pushed back, of course!
To poo sitting in a chair position, actually requires flexing some additional & different muscles, while relaxing others. (Ahem, and that's if we aren't dangling our feet and possible fighting not to fall in, to boot!) To poo in a squat, is SUPER easy. No thinking required, if you haven't lost your flexibility.
The thing is...as an adult you may tell me that to poo standing up is stupid and get stubborn about not doing it, when you've already got this super easy method...but with kids...their NERVES that control their muscles (voluntary & involuntary) have to entirely rewire in order to give them conscious control in the first place. Once that happens though...it takes longer to add different things...like knowing in advance that you're going to have to go soon, holding it while excited, OR RELEASING/PUSHING when your nerves are doing something totally different. It's even hard for adults to change around their neural impulses. Talk to any mountain climber...the first time they had to pee in their clothes. Not an easy thing to do. And we can actually think the whole process through, AND our nerves lined up for conscious control years and years ago. Not until we're in Depends may we really remember what not having 100% conscious control is all about.
If you're determined for the toilet right away (most toddlers using western toilets take a whole YEAR before they poo regularly in the toilet ), you can try having her stand on the seat and squat. Otherwise, patience. This skill too, shall eventually come.
Good Luck