What kind of authority over the other northern lords did Rodrik Cassel have as castellan of Winterfell and a mere landed knight? Would it have been easier to keep everyone in line to resist the ironborn invasion if Robb had had been an adult relation like Benjen to leave the job to instead?

Well, as castellan, he spoke with the authority of House Stark, and Ser Rodrik was able to round up a couple thousand men on the basis of that alone. But yes, I think had uncle Benjen been around as castellan, he would have been able to do things that Ser Rodrik couldn’t – like raise the Northern hill clans.