In The Way of Kings, in chapter 16 (a flashback to seven years ago), it says this:
There was talk of going to war with Jah Keved, once and for all.
Jah Keved and Alethkar are both Vorin, and speak very similar languages. As far as I remember, Jasnah, of Alethkar, and Shallan, of Jah Keved, never mention conflict between each others’ countries in the first book. Why was there “talk of going to war with Jah Keved?”
Please tag spoilers for books other than The Way of Kings.
Including the rest of that paragraph:
And yet, to become a soldier ... The other boys dreamed of joining the army, of fighting with King Gavilar. There was talk of going to war with Jah Keved, once and for all. What would it be like, to finally see some of the heroes from stories? To fight with Highprince Sadeas, or Dalinar the Blackthorn?
The Way of Kings chapter 16
This implies that the boys were daydreaming about participating in a war against Jah Keved, and there's other conversation about going to war to find a Shardblade and becoming a lighteyes.
Other than these children daydreaming, there is other mentions of skirmishes between the highprinces in order to expand their own borders. We know that the Alethi are a highly militant people who have only recently been unified by the Kholins, and before that presumably would regularly duke it out amongst themselves as well as the bordering Vorin princedoms.
There's also the possibility that any border conflict is allowed (or at least, tolerated) under any actual peace treaties between the nations, due to the relative autonomy granted to the highprinces.
Alethkar is a highly militarized nation. Their religion believes that the only point of living is to become soldiers in the Tranquiline Halls. (Technically to achieve their Calling, but the Alethi believed that the best of all Callings was a soldier, so same thing.) That being the case, they literally itched for an excuse to go to war - and they had one in the Sunmaker, the king who originally united all ten princes of Alethela and went on to conquer large swaths of lands, including what eventually became Jah Keved. There was talk of going to war because that was what Alethkar did, and Jah Keved was an easy target. Speaking the same language and sharing the same religion is very enticing from a conqueror's perspective - they're easier to govern and integrate into your own empire that way.
