Is there anywhere in the United States I can get this work done for free? Or on a payment plan no higher than $50 a month?

You're asking for quite a lot there. Most people here will just tell you to seek out your local dental school at your closest university. There they should have appointment information.

I highly doubt you'll find anywhere to do work for free, or a payment plan for $50 a month.

Can you get on your husbands insurance? You say you take care of them, but, you're unemployed?

Here is an option you can try. Take pics of your teeth, good quality pics, and PLEA from the bottom of your heart to /r/personalfinance and pray for a miracle. Sometimes they out of the generosity of their heart will find you a free solution, but this truly is a miracle.

If you go in there bluntly asking for work to be done for free or on a payment plan for $50, you won't get results. You need to make it heartfelt, and be sincere. And be able to prove: 1) Your financially unable to pay for any portion of this 2) You sincerely truly need help and have done everything in your power to seek out solutions to fix your financial situation and are truly out of options.

If you're looking for hand outs, you won't get it. A helping hand for someone who deserves it, you just might get lucky.

Other than that I can't think of any options that meet your criteria of "Free" or "$50/month." You're talking about at least a couple thousand dollars of work likely, so finding someone willing to spread that out for $50/month is extremely unlikely.

If you're lying about your finances and/or can accumulate ANY form of savings, you need to address that.