Haven't read this properly but I kinda get what is going on here, 'how did the Vale soldiers support Jon at winterfell because they couldn't pass Cailin'.
I will tell you how, the Crannogmen know passages through the swamps to pass Cailin, they probably simply asked the Crannogmen to show them routes around the stronghold.
Secondly, Ned stated that Cailin is not fortified fully when not expecting an invasion, 200 soldiers can hold off an army at Cailin but Ramsey wasn't expecting an attack from the south any time soon. Ramsay was probably just using Cailin as a checkpoint fortified by maybe 15 soldiers if that. Such soldiers don't care about their lords, they don't care about politics and Ramsay probably doesn't even know or care who is occupying it. As soon as they saw the Knights of the vale the doors would be slung open with no questions asked. They're not loyal soldiers and Ned stated that Cailin is occupied by Hornwood soldiers because they scouted those lands the most in search for deserters, looters and wildlings. Hornwood not being loyalists to the Boltons the Boltons probably switched their duties and occupied the castle with Bolton soldiers, but again they're not loyal if 2000 cavalry are coming their way they would much rather be alive than to fight for a lord that they don't even care about and visa Vera, the stronghold would simply be used as a checkpoint and border control at the time Petyr passed.
Bolton swords would be dropped at the gates before they had even reached them - also, the castle might not even be occupied. Howland Reed showed his capabilities when taking the castle from the Iron Born, he weakened them so badly and could do the same to Bolton soldiers so I wouldn't be supprised if Cailin was simply abandoned.
