You can look at a related question which has already discussed issues related to compensation and specifically with Frontier Airline:
Having mentioned that. As have already been mentioned in that question the policies related to flight delays or cancellations are set by airline alone:
Each airline has its own policies about what it will do for delayed passengers waiting at the airport; there are no federal requirements. If you are delayed, ask the airline staff if it will pay for meals or a phone call. Some airlines, often those charging very low fares, do not provide any amenities to stranded passengers. Others may not offer amenities if the delay is caused by bad weather or something else beyond the airline's control. Contrary to popular belief, airlines are not required to compensate passengers whose flights are delayed or canceled. As discussed in the chapter on overbooking, compensation is required by law only when you are "bumped" from a flight that is oversold. Airlines almost always refuse to pay passengers for financial losses resulting from a delayed flight. If the purpose of your trip is to close a potentially lucrative business deal, give a speech or lecture, attend a family function, or connect to a cruise, you might want to allow a little extra leeway and take an earlier flight. In other words, airline delays and cancellations aren't unusual, and defensive planning is a good idea when time is your most important consideration.
So if you look at Frontier's policy on the subject:
When it comes to flight delays and cancellations, some situations are within our control and others are not. Here's how we describe the difference:
Controllable Situations are defined as delays, diversions, cancellations, or service delivery failures considered within Frontier's control (such as delayed baggage or flight delays and cancellations caused by aircraft damage, mechanical issues, etc.). If your flight is delayed, cancelled, diverted, or if you miss a connecting flight due to controllable situations, we'll do our best to get you to your destination and place you on our next available Frontier flight at no additional charge. Alternatively, if your flight is cancelled we'll provide you, upon request, a full refund of any unused portion of your ticket.
Uncontrollable Situations are defined as flight delays, diversions, or cancellations out of Frontier's control (such as those caused by weather, Air Traffic Control, etc.). We truly regret that uncontrollable situations may interrupt your travel. Given their nature, we do not offer compensation for uncontrollable events beyond the re-accommodation on the next Frontier flight. Alternatively, if your flight is cancelled we'll provide you, upon request, a full refund of any unused portion of your ticket.
In the event of severe weather such as a blizzard or hurricane, we will enact our Severe Weather Plan and issue travel advisories on FlyFrontier.com. The Severe Weather Plan allows for rebooking of flights without additional fees for a later date when the weather improves.
So the best you can hope for as per this policy is a refund of some sort but there is nothing that I can see in your situation that will warrant that. If the airport is not able to receive flights due to weather or will likely not be able to receive flights at the time of your arrival, which is usually known about 2 hours in advance it will likely to delay you at the source. The situation you have found yourself in where a crew had to seek an alternate airport to land at it highly unlikely to be controllable by the airline. Plus consider the fact that the flight crew had circled Atlanta for 30 minutes and then flown to Knoxville, which is another 40-45 minutes. So they had another hour to spare in their scheduling, which is fine by most standards. Otherwise you will get an Amtrak situation, where a crew only works 3-4 hours a day.