Hi there,
The fact that the bone is healing well (may take a few more months to heal fully), he is painfree and there is no significant leg-length discrepancy are all very positive things!
He's hip hitching - ie he's lifting his hip up, you can even see his shoulder raise on the affected side. this amy be due to weak quads he may not trust that they have teh strenght to bend his knee or they may have been a time where it was difficult to do this due to pain and it may just be a habit.
He probably doesn't even know he's doing it try having him walk in front of a mirror.
i suspect that strenghtening the quads as u are already doing will increase his ability to straighten out the leg fully which will in turn make him feel more secure about weight-bearing fully through that leg.
You sound like very caring parents!
At 9 weeks post fracture I think he's doing very well
Keep us posted on his progress and Happy Holidays!