They prefer it day-to-day. The reason for this is that in aviation you are most likely to get fired from any job during new hire training...the first few weeks when you are learning a new airplane and have little or no union protection. A couple weeks gap might mean an applicant failed out of ground school or simulator training. It would be very important to them to know if you are a training risk.
In your case, I guess you will have to build the most accurate record which you can. The airlines don't necessarily ask for your W-2's, they will want references from all of your employers (or people who can verify self/un-employment). It will be critical for you to line up folks who can attest to the nature of your rodeo days, and periods of off-time.
Hopefully you have some recent, stable, W-2 type employment.
The fact that some companies re-hired you is a good thing...it indicates that they liked you.
Assemble a list of references and do your best on dates. Bring copies (and originals) of as much documentation as you can acquire to interviews. The good news is that I do not think employers would not interview you...you will probably at least get a chance to explain yourself. It might be a good idea to mention your rodeo career in your resume/application cover letter.
Hopefully Lori can chime in on this one...