Hi there. I wanted to respond to this as I have had the EXACT same symptoms as you. My right foot always ends up pivoted outward, and slightly behind the rest of the body. I also feel a lot of stress in the entire right hand side - the hip, psoas, hip flexor, glute etc. Often after a hard days squatting, the right side (especially the hip flexor, the top of the right quad and the right hip) feel tight and awkward. Sometimes painfull but mainly just an unnatural stressed feeling.
I also notice when squatting that thr body/torso twists ever so slightly to the right (so if you looked from the side at the bottom of a squat, the right hip is slightly behind the left).
I wanted to sort it out as it was getting to the point of hurting, and I also felt it in the right hand side the day after cardio like running or cycling. First thing I did is went to a podiatrist. Found a lot of imbalance in the feet, including pronation, hip height and shoulder height. As is often the case, everything in the body is linked (in my case the right hand side is 'plagued' all the way from the foot to the hip to the lower back, including ITB syndrome in the right knee).
I got orthotics (in-steps), both for everyday wearing and large ones for gym shoes. At the same time I am getting treatment on my back - and THIS IS WHAT I WANT YOU TO TAKE NOTE OF - as these imbalances, which I left to go on for way too long, caused a lower back injury. In particular, inflammation of a lower vertebrae/disc. That is what was causing a lot of the associated pain in the hip, hip flexor, buttock etc. I am also self-treating the hip flexor and other ligaments in that area which have becomes very stressed over time (the area between the top of the quad and the lower abdominal region).
In summary, I would put the neccessary money aside to see a) a podiatrist and b) a chiro. It is well worth it. Don't leave it for too long (as I unfortunately did) as it causes a lot of damage, which cannot be prevented just by stretching/strengthening as it has to do with structure, posture and movement stemming from the feet and back.