While some billing companies will hire people to work from home, it is not common, and usually you have to have a proven track record (experience) in most cases. The biggest issue is how people look at what "work from home" means. Generally, it means you are working as if you were in an office, but at home instead. No kids to deal with, no distractions, HIPAA compliant work-space/internet connection, etc.
In addition to my regular work running a medical practice, I also work remotely for two billing companies. The reason I was hired with both was I had 20 years experience in my specialty, I have no kids/other obligations during the hours I work for them, and I am able to be HIPAA compliant with my work-space. This is not easy to do for most people.
You say you are already limited with your hours at your job due to your particular situation. Can you tell a potential remote employer that you will be available when they need you to be available, with no other commitments? Meaning, if they need you to do billing for a client from 7pm-10pm each night, you can do that, with absolutely no personal interruptions, just like if you were in an office setting? If the answer is no, then remote work is not an option.