Is it legal to possess in the "other" state? If so, and you are just in transit then one would hope some discretion would be used by the officer and nothing would come of it. "Technically" you are supposed to have a 5320 for each item with destination and approx time/day it'll be returned home when leaving the state listed on your form4/form1's.
I take mine to the family farm during the summers so fill out 5320's and list the dates to cover the whole year and just do it every year. Pretty painless and completely legal. Always better to error on the side of caution with all things firearm related.
If they are not legal in the neighboring state, I would say leave them home and not take any chances at all. If you are traveling "through" a state that prohibits private ownership, as long as you have the signed off 5320 you should be just fine.
I live in Ohio and my parents live right across the river in Ky. On the way home and i cross the bridge from Ohio to Ky I stop by my parents in ky before getting home in Ohio.
Well it doesn't look like NFA (ownership) is restricted in KY so chances are you are just fine. Personally, I'd do the 5320 and list transport to your parents address, date it for the whole year and be worry free. The form is free and could take a month (typically) at most to get approval.