How long have they been roosting? At 12 weeks, roosting may be a new event so this could be teething problems. But it could also be a sign of future problems. They are still fairly small, they will get a lot larger. And they should just be hitting puberty. At least they are all the same age.
Coop space could be part of the problem and might be important to know, but since it is a roosting issue I'm more concerned with roosting space. How much roost space do you have and how is it arranged? Do you have enough room for weaker chickens to separate themselves from bullies?
My chickens get along fine during the day but when they are going to the roosts they can be pretty brutal to each other. The ones highest in the pecking order get to sleep where they want. If a lower-ranked bird is in their way they knock them out of the way or peck them. If they don't like the chicken that is roosting next to them, they peck them. My adults do that, let alone the immature ones. Often it is the adults being brutal to the immature but not always.
Sometimes the ones being pecked try to find a safer place to sleep. That might be your nests or some other place in the coop, even the coop floor. I have had chickens leave the coop totally and try to sleep somewhere outside. It's possible your leghorn is being bullied on the roosts and is looking for a safer place. It's possible she just prefers the tree. It could be something else but those two are my first first guesses.
If the problem is that she is being bullied on the roosts putting her on the roosts doesn't seem like a great solution to me. She's still going to be bullied if she tries to sleep there. That's why the interest in your roosts and how they are arranged. It may be beneficial to put in a separate roost separated a bit from the main roosts to give her a safer place to go. I have seen a bully walk along the roosts to go peck a weaker chicken. It doesn't happen that often but all it takes is one bully. I've also had one chicken take a specific dislike to another specific chicken. They are fine with all the others but seek out that one to bully.
My suggestion is close to Centrarchid's first suggestion if you don't have a run to lock them all in. Lock her in the coop for a few days to get her imprinted on the coop as a place to sleep. She was already imprinted on the coop so look closely at roost space and arrangement.
If you have a run with that coop where you can lock all 15 in there and she can't get to that tree, lock them all in the run for a few days, maybe a week or so,. Try to break her habit of sleeping in the tree. If she tries to sleep in the run instead of the coop, lock her in the coop at night. See where she chooses to sleep.
I'm assuming the problem is that she is getting bullied on the roosts. That may not be the case. She may just prefer the tree. It may be something else. I really don't know.
If roost space is an issue they will grow a lot. If it is already tight it can get worse as they get bigger.
At 12 weeks they are just hitting puberty. They will mature at different rates so the pecking order could be adjusted as they age. Oh, living with teenagers!!! Expect growing pains and some disruptions, even if it is an all-pullet flock. If you have a cockerel or two in the mix it can get even wilder. Sometimes it can go really smoothly, this may be the worst you see. Sometimes it gets really frustrating. Usually once they all mature it becomes a nice flock.