I'm not an attorney, and I'm in California, but unfortunately, I think it may be true that you don't have a very good case.
If you are asking for divorce, you are asking the court to dissolve something that was never legally recognized in the first place.
Many states do not recognize common law marriage and even at that, you have to prove that you were recognized, not just by acquaintences, but by banks, health insurance and other agencies as "married". A shot record with both your names is not legally binding.
Having an 18 year old child together is not the same as being married in the eyes of the legal system.
I don't think that any type of agreement for your ex to pay you support will be upheld either based on the fact your youngest child isn't his.
I know of someone who went through this not too long ago. The dad on the birth certificate turned out not to be the father after he had been ordered to pay support, and had done so. Another man came forward and wanted rights to the child and he turned out to be the bio father. The guy on the birth certificate was aced out as far as any rights, which hurt him, but also of any obligations, which meant he didn't have to pay anymore.
I think counselling is a good place to start, even if your ex won't go because you do have a child in the midst of all this.
You need professional advice on how to deal with explaining why "dad" isn't coming around anymore and at what point it's appropriate to explain all this adult stuff to a kid. The child needs to know that he's no less loved and no less of a person because of all this.
That should be your priority. And, if your ex isn't willing to still show love for him, you'll need that help more than ever.
Your son still has a mom who loves him, he still has a brother. Hopefully the only person he's known as his father won't abandon him entirely. He may just need some time to cool off and realize his love for the child goes beyond all this.
I wish you the best. But get some counselling referrals.