I fly Frontier on occasion and find they are much more reliable than the other ultra-low-cost carriers. That said, you would have to be crazy to book Frontier in a situation like this.

They have an extremely limited schedule, virtually no back-up planes available, and they do not interline, so if your flight is cancelled or has a long delay, they will not put you on another airline.

You need to get to your next city to catch an international flight. Take a legacy carrier that has numerous back-up options in case weather or ATC or mechanical issues strike. And give yourself plenty of time, just in case.

Do not EVER take a non-interlining ultra low-cost carrier in a situation like yours. (Southwest, which does not interline, is the exception, because they have so many flight options in the event of an IRROP. I'm saying stay away from Spirit, Allegiant, and Frontier) Trying to save a few bucks can cost you hundreds - or more - and can be very bad for the digestion.