Theres no "lower jaw expansion" method like MSE/MARPE or SARPE exist for the maxilla because the mandible doesnt have a midline suture (it does but it fuzes in your first year of life so you dont have an open one), the teeth sit on one continuous bone so a palate-style expansion is impossible.
However there are surgeries like MSDO where your midline gets cut open and a distraction device widens your jaw while new bone forms in the gap. This is probably the closest you can get to 'palate like expansion' but its usually limited to between 4mm to 8mm and can damage your teeth and nerves.
You could do an orthodontic approach like dental tipping which will flare your teeth outwards but this again has very strict limits and it wont change your skeletal structure.
I didnt completely understand the problem here so if its not the bite but just the jaw itself you could do Jaw angle Implants, other custom mandible implants or fat grafting to widen your jaws appearance. Alternatively BSSO for repositioning, Genioplasty for reshaping.
Your maxilla usually doesnt influence your mandible that way but if its extremely wide your lower teeth/jaw will obviously look extra narrow