That is irrelevant. In a free market a hospital would tell them there is nothing they can do and ask them to leave. If they didn't have a place to go they would suggest the closest religious or otherwise voluntary non-state funded homeless shelter. If they still wouldn't leave then they would use private security to escort them off of the premises. What they wouldn't do is put a crippled mother in jail.
Bull fucking shit you choose your own doctors, you are living in a dream land. Your insurance company chooses them. Your insurance company paid millions of dollars to elect Obama, you actually believe there is ANY semblance to the free market within our health care system?! Free market health care is a lot more than people paying for their own care, it would allow people to pay for WHATEVER care they wanted HOWEVER they wanted rather than the government contrived medical establishment that tells us what treatments we are allowed to have.
I pay for my own insurance and I get a list of like two doctors I can see. I pay for my insurance through my company because it is all tax deductible for me and my company. If I could get tax deductible insurance outside my company or better yet if they decreased the tax rate significantly and ended the tax deductible corporate health care system we have then I would opt for a higher salary and I would get my own catastrophic health insurance plan. Then I would go see doctors who utilize the types of medicines that work best for me (natural medicines). They would get more patients because the government wouldn't prevent them from advertising their medical claims, so the market can test those claims and bring the prices down through competition.
Right now there is zero competition because the FDA and the AMA completely control medicine, and they are run by the same people who funded Obama's campaign. Look it up.