It sounds like the colliders used in detecting hand-object intersection may be temporarily disabled whilst holding an object. This may be part of SteamVR's interaction script logic. I don't recall off the top of my head how the latest SteamVR rig operates; however, within the SteamVR rig hierarchy, I would take a look at the specific script components that react via OnTriggerEnter(), such as any "on grab" logic, and see how they act on colliders they reference. There should be a script API within SteamVR's rig package where you can register a listener to an "on grab" event. You can use this to troubleshoot, or enable/disable your own custom colliders used specifically to handle any further collisions on held objects. Ideally, studying SteamVR's API and interaction scripts will inform you about what happens to hand colliders OnTriggerEnter (they will likely have a Rigidbody component attached to them in the prefab hierarchy, likely set to be kinematic).
As for objects getting flung out from inside another: it sounds like both objects in question may be non-trigger colliders. Trigger colliders can pass through one another (assuming no additional script logic acts on them to do otherwise), whereas non-trigger colliders will separate upon impacting one another, preventing sustained intersection. A bouncy ball for instance can be realized with a rigidbody component using gravity and a non-trigger sphere collider, such that it bounces away from a non-trigger floor collider upon impact, producing an OnCollisionEnter() event. If the ball were a trigger collider instead, it would invoke an OnTriggerEnter() event upon passing through the floor collider, but it would continue falling through it.
In your case, it may be that a non-trigger collider is placed inside another via SteamVR's "object hold" interaction script, allowing for such placement during an object grab and hold (perhaps due to it disabling the object's collider component temporarily), but restoring non-trigger collision behaviour on the object upon its release, causing the released object to fly out.