You might have standing to pursue a negligence claim , but you also need proximate cause. Your best bet may be to get a workers' comp lawyer and look into that angle. The fact that the companies claim you are an independent contractor does not make it so.
You need to hire the best, most aggressive workers' comp lawyer you can find. This week. Don't delay any longer. The insurance company will not do anything for you unless you have a lawyer to make it happen.
If you are a trial lawyer, you will find yourself working all weekend the weekend before the case is set for trial. Then if the case is not reached or it gets postponed, you will work another weekend when it comes up again. This is very stressful for the lawyer and tough on the spouse and kids too. I agree with my colleagues that just about all attorneys put in long hours and endure a lot of stress, depending on their practice area and the firm for which they work.
I agree with both of these answers. One of the biggest obstacles to showing that you were fired for an unlawful reason is being able to prove it with a document. Employers usually do not document their improper motives in your file when they fire you. Because you have filed a workers' comp case (and make sure you actually have; you need to give written notice of the injury to employer within 30 days and file Form 18 with the NCIC as well) then you can request a copy of your employment file...
The employer probably cannot exclude you from the group health plan without violating federal law, so the answer is yes, they can sign you up for it. You may be able to exclude yourself from coverage. You will have to ask them. Of course, having health insurance coverage is a good thing, so think carefully about it before you opt out of coverage.
If your employer of injury cannot accommodate your restrictions then they owe you TTD payments (assuming they accepted liability for your claim). If your new part time position can only provide 10 hours work per week then they probably should be paying TPD (temporary partial disability) to you. If you are not getting a weekly wage loss check from the insurance company then you need to talk to a workers' comp lawyer. You need to protect your legal rights.