This. I’m glad our family is an “open” one rather than a “keep secrets” one. I’ve seen the other type from my dad’s side and it only leads to a lot of hurt, almost always due to misunderstandings.
The quickest way to solve a problem is to acknowledge the problem and discuss it. Misunderstandings fall away, so many can be easily solved, and if not, then at least you know what the real problem is.
It’s not up to the OP to solve the issue - that’s on the sons - but it would be really good to pull the curtain back (nicely) and let the issue see the light instead of covering it up and letting it burn/grow.
Just because two people are adults doesn’t mean they always know what to do.
Personally, I wouldn’t even keep any secrets. I’d let both sons know what I know (separately to not start confrontation) and tell them they need to discuss it together to get a working solution. If oldest doesn’t have the money for the painting he should return it.