The River Between Us, eh? Not to blow your mind or anything, but there's this river, the Mississippi, and it seems to come between a lot of people in this book. Shocking, we know.
Geographically, the Mississippi River forms the border between Illinois and Missouri (and a lot of other places, of course, but we're concerned with these two). Tilly says, "Even though Tower Rock was over in Missouri, with the river between us, it gave our town its name: Grand Tower" (2.3). Right away then, much as the river divides, it also unites—Tilly's town in Illinois is named after a feature from across the Mississippi.
With Howard Leland Hutchings and his family living over in St. Louis, he's never even met his dad's family on the Illinois side of the river, so the river literally stands between the two narrators, Howard and Tilly. Again, though, we see they come together anyway.
From a historical perspective, the battle Noah fights in is for control of the Mississippi River, which both the North and South need. And, if we look at the flow of the river, it runs between Grand Tower and New Orleans, or between the Pruitt family and Delphine and Calinda. That river is all up in everyone's business. But, most importantly, time and again it unites as much as it divides.