The only way I have figured out how to manage people who are very different from me is to try to figure out what motivates them, so that I can understand them better and try to view them empathetically, even when I don't get it myself. For example: nobody actually cares only about money. They may care more about money than you do, or for different reasons, but it's not actually about the money -- it's about how the money makes them feel. So you need to figure out what that is and why. Did he have an insecure childhood and now craves the security that money brings him, or now wants to have All The Things that he never had? Did his parents teach him that status is the most important thing, and he figured out that throwing money around is the best way to get that? Or is he just an accountant type who likes the sense of order and control he gets from tracking his finances? Etc. If you understand where he is coming from, that puts you in a better position to take his annoying traits with a grain of salt (e.g., you can feel sorry that all he learned from his parents is XYZ, instead of getting angry that he once again did ABC because money). It also helps you communicate with him more effectively, because you can learn how to speak his language. Because the way you "win" a negotiation isn't to convince the other guy that you're right and he needs to back down -- it's to convince him that your approach is a great way to get him what he needs.
My only other suggestion is don't borrow trouble. Your in-laws trust him to handle their money, so he has provided them some reason to do so. Maybe he's actually good at it. Maybe they think he shares their values, even if they don't align with yours. Etc. It doesn't even necessarily mean he's their favorite person; heck, in my will, I put my brother-in-law in charge of the finances for my kids -- he and I don't see eye to eye on a number of things, and I could never live with him, but he's a CFO type, and I trust him implicitly to make sure my kids are supported and their future inheritance is managed properly. Trust that your in-laws also had a reason for doing what they did, and trust them to exercise reasonable judgment on the matter. Because, really, it is their money, and they have the right to do whatever they want with it.
And that means respecting your and your DW's limited authority in that matter. This is about your in-laws' best interest, not your DW's potential future inheritance. Yes, he may decide to spend the money in a way you and your DW don't agree with. But it was the in-laws' choice to give him that power instead of you or your DW. So you need to adjust to his role as the guy with the right to make those decisions and train yourself to ignore anything short of abuse or theft.
My one practical suggestion is that the in-laws should consider writing up some process for breaking a tie. Because when you have one person in charge of making the decisions that require spending money, and a different person in charge of authorizing those expenses, you have a built-in stalemate, with no way to resolve it other than going to court -- which will likely take too much time AND all of the available resources. So perhaps they could add some language specifying that if the two disagree, then they will get a medical opinion, and both sides have to follow the doctor's advice, or something similar.