Who made the determination that you "obviously need surgery again"? The only obvious course of action is to have it examined to determine what state it is currently in.
If your knee "feels very unstable and its painful at times" then it is NOT "as strong as it ever was." You may be able to rehab/train it to be as strong as it was prior to the trauma. This depends on the severity of the injury, your dedication to rehab, how intelligently you train/prehab/avoid contraindicated modalities, and your ability to avoid unintelligent behavior. Of course, a little bit of luck plays a role.
So, if you actually have your knee examined (don't be shy about second or third or more opinions) and go through the rehab process, you can then worry about squats vs leg presses.
Get this straight. If you refuse to go through the first two steps described, your chance of re-injury is a near certainty.
Let's say that you've tempered your youthful impatience and actually did those two things. And now you're ready to move to the next step. Here are my thoughts.
One of the fundamental differences between a squatting pattern and a leg press pattern is the former allows the pelvis to move more freely. This allows the quadriceps to act as knee extensors IN CONJUNCTION with movement at the hips.
A typical leg press, because it inhibits this, places greater loading at the knees. You can minimize the load on the knees by placing the feet higher on the platform (think of the typical 45 degree leg press machines). This will shift the load towards the glutes and hamstring complex. Easier on the knees with less work done by the quadriceps.
Does this mean no more leg presses in your future? Not necessarily. There is a continuum in which it's beneficial to have the stability that a machine provides. All machines are not evil. Some have their time and place.
As a part of your rehab and into your training life, you must be constantly aware of growing stronger in all three planes: frontal; sagittal, transverse. This means take a macro look and understand how the hamstring complex, the adductors/abductors, glutes, the core, as well as the rest of your body contribute to a clean beneficial squat. There are many exercises which address this and to describe them all is beyond the scope of this post.
In fact, my stance is that most people need to EARN THE RIGHT to perform the traditional squat. Those who have compensatory movement patterns, overactive/underactive issues, lifestyle choices, postural limitations, the reasons go on and on, etc. have no right to perform the traditional squat in an aggressive manner.
Until they earn this right, they must explore other options in a squatting pattern. And even after they've earned this right, they should still incorporate it into their training (just how much and how often is individual dependent).
What's interesting (as well as maddening to see everywhere) are those on the other end of the spectrum who completely blow off the need to strengthen the less glamorous muscles or learn the more challenging exercises and go straight to the machines. Why bother learning the RFESS when that pretty and shiny leg press machine is right there...? Who gives a shit about the popliteus when it's those VMOs that gets attention?
1) Get that knee examined.
2) Go through the rehab.
3) Even after rehab, integrate into your training getting stronger on all three planes I discussed. You (along with a large segment of the population) have some imbalance that needs to be addressed. It's a never-ending quest, really. A classic mistake I see often is a lifter who continues to do rotator cuff work with 5 pound dbs even though his main lifts are getting stronger. Big mistake. If the rotator cuff is the weak link (as they usually are with most people), it's absurd to not strengthen them as the prime movers grow stronger.
4) As the less glamorous muscles grow stronger, know the point at which too much stability work within a workout or a cycle can actually stifle your hypertrophy goals. One example would be lifter who does work requiring more stability and then follows up with work in which stability is not an issue (i.e. machine-based ). This also hints at the importance of pre-exhaust as well as the continuum between stability-intensive movements and those in which stability is less of a factor. Keep in mind that you must be healthy in the first place to even contemplate this and knowledgeable enough to know just where on that continuum you should focus on.