I bet you’re wishing you had settled this before you were married. Me too. It’s much, much harder to negotiate situations like this after the fact. It’s not impossible but it’s harder. Your husband has raised his kids well into adulthood to expect that they don’t have to be responsible for themselves. Although your position is not at all unreasonable, it may not be negotiable.
The silent treatment isn’t helping the situation one bit. The two of you need to have one of those difficult conversations to clear the air and set some rules. Your husband wants to give his kids the benefit of the doubt. That’s understandable. But the most important question, I think, is whether there will be enough money for the two of you to retire if the kids don’t pay up. If not, it’s time for a change.
It’s probably pointless to talk about this as a matter of building the kids’ character. You will have more success if you focus only on your future security as a couple and develop a financial plan accordingly. Fortunately, you are only in your 40s and you have some time to build a nest egg. Figure out your financial goals and what you’ll need to do to reach them. It will probably become self-evident that you can’t keep adult kids on the payroll and get there. The goal is for the two of you to be on the same team, building a retirement, instead of being on different teams and fighting about his kids.
By the way: If your husband decides he needs to learn to say no to his adult children but can’t figure out how to do it, there are many, many websites that will give him some pointers. He’s not at all alone in dealing with this problem. Search using key words “adult children, money” and you’ll probably be surprised at how many sites come up.
I wish you well.