I don't know anything about acting, but I have a few suggestions for jobs that are flexible and may be able to fit your needs.
You may want to look for jobs that people can do remotely, on their own time. For example, there are some reputable survey websites where you get paid a very small amount for each survey you take. There are also companies doing market research that sometimes hire people to go into stores and take notes on their experience. These are just small examples, but this type of remote job might be what you want to look for and/or ask a guidance counselor about.
How close are you to where you'd have to audition? Assuming you're pretty close, you could also look into part-time evening jobs, like waitressing, retail, or working at a movie theater, if your auditions would all be during the day. These might be more lucrative than the specific examples I posted above (surveys, market research), but other remote jobs may pay better.