if your trying to "turn" your kids into Bills fans, and are going to go to the games and NOT tailgate, then your doing it wrong man....tailgaiting is not just for getting drunk and rowdy (although thats what I do)...tailgaiting is for grillin some food, taking in the atmosphere, walking around and being immersed in it - vendors, watching others, doing the whole bills fieldhouse bit....your kids will easily become bills fans when they see the passion of the thousands of other fans
Ive been a season ticket holder for a long time, and have parked in private and official bills lots....and I strongly recommend going with Bills lots...only for the simple reason your right in the thick of it all...I have never once had an issue getting out of the lots (I also dont hang around and watch players celebrate/run off the field/take my sweet ass time getting out of the game)...once game ends, leave your seats and have a nice quick walk to your car and you'll be back in amherst in 30 minutes at most...park in lot 5 and you will have no issues what so ever...drive for 5 baby!
(just taking your kids to games is to rob them of the season ticket experience)