The kind of test you're describing sounds like the normal joint gap that's present when pressure is applied. Usually there is slightly more movement on the outside edge of the knee joint compared to the inside. There's also more motion when the knee is bent compared to when it's straight.
When the knee is fully straightened, it's called the closed-pack joint position. That's the most stable position of the joint so it makes sense the joint gap or laxity is the least in this position. The opposite is true for the open-pack joint position (flexion).
You didn't say what kind of operation you're having. If you've torn the ligaments and you're having a ligament repair, then the surgeon will try to restore your normal joint laxity. With a joint replacement sometimes the ligaments inside the knee are kept and sometimes they are removed. The kind of implant you get depends on whether or not you still have your ligaments. Again, the surgeon tries to balance joint movement to mimic normal as much as possible.
This would be a good question to ask next time you have the chance.