I am trying to play through the traditional opening but with my mods installed the opening carriage to Helgen wigs out hard. I can hear the sounds of something attacking and the carrige is flying and tumbling around; never actually makes it to Helgen.

its generally best to activate mods after helgen sequence many mods performs startup checks that can also put stress on engine during opening scene which is very important for vanilla start.
some mods i can think of which causes problem with vanilla start
Better vampire appearance mod
Helgen Reborn
i had a problem with sofia follower mod as well when i forgot to turn it off during start and noticed problem with horse making noises and when i deactivated it problem was solved so maybe that mod too.

Posting your load order would probably help. Asking, "What mods mess with the opening sequence?" is kind of like asking, "Which person clapped 1000 times?" Well, any one of the can do it. Which ones are you using?