Booking a return flight from LIH to home in BUF. Prices from LIH to BUF, routing through JFK, are 30% higher than the exact same flight if I book it in 2 legs:

LIH->HNL->JFK->BUF: $1,001


LIH->HNL->JFK: $489
+
JFK->BUF: $224
-------------------------
$713

With our family of 5 that's a $1,500 difference.

Is there a reason this is priced out in this way? Is there anything preventing me from simply booking these flights independently? Any risk, if we're not checking bags?

Also, and this may be a dumb question... if I purchase those legs separately I can go directly from first leg to the 2nd leg without any issues with TSA, etc correct?

If I did check a bag, would I (only one person from my travelling party) need to leave, recheck the bag, and come back through TSA again?