Bicycle design for a crooked hip
Similar to the other answers it would be worthwhile getting a professional to assess your current bike fit (and potential modifications that may be required).  If possible I would suggest a sports physiotherapist that specializes in bike fitting. They exist, I have used one before.  A physio will be best qualified for assessing how changes in position can affect your hip and knee functioning.  While many bike fitters have some training (and often good intuition), dealing with severe dysfunctions may be out of their area of expertise.  Alternatively, you may need to facilitate a relationship between your physio and bike fitter if you cannot find a single person who can wear both hats. 

To give you hope that it is possible to tweak a standard bicycle here are some things that could help (with the right guidance):


leather hammock saddles (e.g. Brooks) break into a custom form fit for each rider. During the break-in phase you are physically tearing the taut leather until the pressure is equalized across the saddle.  This results in custom form fitting that can accommodate different pelvic tilts and orientations.  Be warned however, the break-in period can be long (although water break-ins can speed this up considerably at the cost of leather longevity).
Shoe shims exist to help angle the foot differently to optimize knee alignment. Also foot orientation on the pedal can be used to help modify knee tracking.
Shoe shims can also be used to accommodate for structural leg length differences.
You may consider flat pedals over clip-less so that you can continually modify your positioning to reduce the likelihood of repetitive stress injuries.