Be sure to add banded clamshells into your program.
Keep the band ABOVE the knees as this will greatly reduce any chance of irritation to that area.
Exercises such as banded x walks may be better suited as a progression to help integrate the glute med/min. The reason I’m not a fan of pushing a load to the side with the foot is this has the potential to irritate the LCL. You’ve already got issues with the patellar tendon. Why throw more wood on a fire your trying to extinguish…?
As your recovery improves, you also may want to incorporate staggered stance RDLs holding a weight (db or kettlebell) in the contralateral side. Instead of a pure uni-lateral RDL, the non-working leg is placed behind and slightly out to the side for a modicum of stability. At first, use that back foot as much as necessary to maintain good form. As you improve in technique, intermuscular coordination, etc. keep that back foot in contact with the ground but place as little weight on it as possible. A cue I often give is to imagine a cracker between that back foot and the ground and to not break the cracker.
Obviously, the logical progression from this is the standard uni-lateral RDL with a db or kettlebell on the contralateral side. If possible, I prefer the kettlebell as its shape lends itself to a more balanced feel. And the reason I have the individual hold it on the contralateral is side is because that weight will try to twist you in that direction. By resisting this twist, your glute med/min are being recruited.
I’m going to remind you to start with the least aggressive movement such as the clamshells. Progress only when you are certain and progress in the most conservative manner. The kaizen principle doesn’t just apply to hitting PRs.
Someone mentioned that you should stretch the rectus femoris and this is good advice. I haven’t read every response to this thread but be sure to incorporate smr work as well. And not just the obvious spots such as the IT band. You also want to address the vastus lateralis, medialis, rectus, sartorius. Finding and addressing trigger points can be tricky so you’ll need to be patient. The most common sequence is general warm-up, smr, static stretch, rehab/prehab movements to integrate. Variations in this sequence are individual specific.
As for becoming more efficient at recruiting the VMO, I’ve had great success with TKEs in the people I help. Add light taps to the area with your finger tips as your performing them; this can increase neural efficiency. The VMO is a key player in many patellar tendon issues.
Another very little known technique I’ve applied to help others is to strengthen the popliteus. This small muscle can often be a key player in stability. I don’t know what type of equipment you have access to. But most have access to a cable station. You can try clipping a stirrup type of attachment and performing unilateral standing leg curls. Be sure to place both hands on for support and place the non-working foot on the ground firmly for support. I often recommend this over the machine leg curl for two reasons: 1) for rehab/prehab purposes, I lean towards some movement at the hip in conjunction with movement at the knee; 2) the machine would have to fit you damn near perfectly in order to prevent other issues.
And safely performing exercises that target flexion at the knee will contribute toward stabilizing the knee. Anyone who says that you do not need to perform variations of the the leg curl (in which the primary focus is flexion of the knees) is ABSOLUTELY WRONG. I already mentioned the popliteus. Also, there are movements in sports that rely on flexion at the knees with minimal movement at the hip. For example, a mountain bike racer who needs to climb a steep sandy hill must keep his butt on the saddle (to prevent the rear wheel from washing out) and he must apply a circular force to the pedals (again, to prevent the rear wheel from washing out). This is just one example. And let’s not forget the biceps femoris short head, due to where it originates and attaches, is next to impossible to train with movements such as RDLs, stiff-legged deads, etc.
Knee injuries are mercurial and I (as well as others on this thread) have only scratched the surface. If you are serious about resolving this, you should consider giving updates with possible video.