I'm sorry to hear that your marriage is under stress, that you live in fear of someone you know stealing from you again, and that your step(?)-son's life is in jeopardy. This is a highly stressful and emotional time for everyone.
First off, this is both your money. Is spending it so that someone doesn't have to do anything but look for drugs and get high really earn either of you or your wife money or give you a sense of satisfaction or even keeping this man safe? Heck no. So I'm not sure what the rationale is.
If he was going for treatment somewhere, and your wife was paying for it (meaning you were both paying for it), I'm sure that would be a different matter entirely.
Here are some facts to consider though:
1. This is your wife's son. Even if he hits rock bottom, she will never stop loving him. Your wife should go listen to what others have gone through so she can see this is actually nothing new that someone has experienced as a parent. She will also learn that cutting the child financially off and to stop providing for a drug lifestyle is a good thing.
2. Handing your wife an ultimatum to make a choice will not work. You can not make someone choose. You can try to convince them, but they must take responsibility and you can't control people. You can only control yourself.
But you can negotiate, just like you negotiate anything with a partner in marriage.
This is a stressful negotiation, so figure out your BATNA:
Best Alternative To a Negotiated Agreement. The BATNA for you might be to leave your wife if nothing changes, or even call the police to have her arrested for purchasing drugs (she is giving money to an individual for the purchase of drugs, isn't she?). Write your BATNA down, memorize it. You will feel better knowing you have a plan, and that you are not completely reliant on others.
This is the important part: do not ever reveal your BATNA unless you are not making progress during the negotiation. If you are still talking, exploring different solutions, then that is fine, but as soon as someone says they do not want to talk about anything, or there is no arrangement that can be made, mention your BATNA and be prepared to run with it. If they do not budge, then run with your BATNA.
Before you start discussing anything with your wife, ask yourself what would be the end-state that both of you would like: for her son to be off of drugs, not to give money for drugs, not to be robbed, etc. Ask questions on how to get there.
Next, do the exercise with her. And make sure that it is an open discussion. Also, if emotions get running high, set a rule that either one of you can step away for 15 minutes to come back on time. But either must walk away for a bit.
Some solutions might be: Keep supporting the son for another 3 months, and if by that time he is not working enough to support himself, the son will not be given any more money; don't give the son any money for rent, but give it to go to rehab; don't give the son any money until all the items are returned or replaced; etc.
There are tonnes of options, but your main goal will be to keep your marriage intact and loving, while keeping your home safe.
Best of luck