My family of 4 is flying on Jet Blue's All You Can Jet pass.

Dilemma #1
We are booked on a flight which arrives JFK at 6:30 pm from St Lucia(UVF) on September 12. We must then try to make the connection to LAX on a flight that departs at 7:52pm. Is 1 hour 22 min enough as long as we don't have checked-in luggage?

Just in case, we are also booked on a back-up flight that departs JFK at 4:55pm the next day, but I would prefer to not spend a night near JFK.

I would just keep both flights out of JFK, but if we cancel w/in 3 days of departure, Jet Blue assesses $100 per person penalty, so we have to decide which flight to cancel. On the other hand, paying $400 in late cancel fee is almost the same as paying for 1 night at a hotel near JFK, so I might just keep both reservations just in case we can make the first connecting flight.

My other option is to take a connecting flight to Austin, TX which leaves JFK around 8:30pm on September 12 so my 5 year old can finally see the city that shares his name.

Dilemma #2

We are on a flight which arrives JFK at 6:01pm from CUN(Cancun) on September 26. Our connecting flight to LAX departs at 7:52pm. Can we make it w/o checked-in luggage?

Add'l info: My kids are 9 and 5, and they are both experienced travellers so they won't slow us down.

Any thoughts or advise is gretly appreciated