I am looking at purchasing tickets from PHX to AUS on Frontier, and also from AUS to FLL on Jet blue on the same day. There is a 1 hr 50 minute layover. I will be traveling with my wife and 2 young kids. The question I have is do all of us have to go back through security or can I leave my wife and kids at the Jet Blue gate (19) after getting off the plane, then collect the bags myself and check them in alone. And is there enough time to do this?