Alternative schools can be a wonderful option for students who are having trouble in school. Your son might be acting out if he has been struggling with his studies for quite a while and also concerned about your well-being. Considering your health problems, homeschooling does not seem to be a good option.
I urge you to make an appointment with the school counselor and others who are suggesting the referral. Have your son present. Find out all you can about why the school is suggesting that he be referred to the alternative school. Is it just his behavior, or are they looking at a learning environment more suitable for your son -- one in which he can get more help in his studies? If you haven't done so already, the first step is testing your son for learning disabilities. Is the alternative school the least restrictive learning situation for your son?
My experience has been that alternative schools are often life-savers for students, but check it out first before you agree to the placement. Request a tour of the alternative school for you and your son. Set up a meeting with the alternative school counselor to discuss the advantages of a transfer. And finally, make sure the school is really "alternative" not just a warehouse of misbehaving students.