Your husband is an adult, just as you are. He can go to therapy, or not. There's little you can do to force him to go. However all is not lost. Here you will find invaluable peer support, a variety of suggestions, strategies and skill sets that may very well improve your relationship to a greater or lesser extent. You'll have to agree that educating yourself about these ongoing issues and improving a variety of skills can only help.
As I wrote above, you too are an adult, you too can make choices to improve your life. Exactly what will those will be remain to be seen, they're up to you. Surely as you learn more, get peer support and see ways to improve your boundaries, life won't feel as distressing as it does now.
Him telling everyone you need inpatient treatment is typical blame-shifting, trying to take the focus off himself and framing you as his scapegoat. It's also called projecting. Not fair, not right, and hopefully those people who really know you won't be conned or fazed by his badmouthing and distortions. I recall when my now-ex and I separated that she started making all sorts of horrible allegations and I see now she was trying to make me look worse than her. It worked to a limited extent at first but long term she lost credibility with those who counted in my life.
Also, unless he has adopted your son, he has no legal rights as parent to your son. Legally. Doesn't mean he can't influence him negatively.
I want out.
Well, you posted on the Staying board. We have other boards too and you're welcome to post on whichever ones are best for your questions and goals. Here on Staying there are many communication and coping skills described and taught. Take advantage of them. Doesn't mean you have to Stay permanently. If you wish you can view it as "Staying For Now". We also have "Leaving" as well as "Family Law", among others.