Not saying this manga makes sense, because there are several plot holes, but it leading to war is at least plausible. First, her father is literally the "minister of war" or something equivalent. It means her family is in charge of a lot of decisions not just in war but in regards to peace talks and negotiations when it comes to treaties. It would absolutely make sense that other countries would want to manipulate their politics (in this case, the heir) in order to benefit themselves.
That said, there's still a lot of holes in her vision. Who's this supposed sooth sayer? Why is she so sure they are telling an accurate prediction? After using magic on herself, why is she still not questioning that future, which supposedly comes around because she's not suited for magic? There's a lot of questions and will likely never be answers.
How can just a heir position of a family can lead to war in a country?#－.－) If their sibling's relationship is good then she could just give up on the position, i mean if she really try to oppose it then i don't think that orther can have any ideas. And more, she said that it also involves other countries in the power struggles, then why don't she think the war was because of someone else's scheme and even if she run away, the family and the country will still be in danger, just that they will have another reason for it.