Assuming, the empty weight is around 1700 lbs, and your max is 2800 you
have 1100 lbs to play with. That airplane has an airspeed of about 135 kts. In still wind conditions, you can do your trip in just over 2 hrs. that normally aspirated 182 with its 0470 engine properly leaned will burn about 12 gallons per hour. but for safety's sake plan for a 14 gph burn. If you take 40 gallons total you gain another 120 pounds of cargo carrying capability and you land with 1 hr of fuel in the tanks. your fuel weight would be 240 lbs giving you 860 lbs for your family and bags. I have a 1968 182 and it is perfect for my family. there is nothing wrong with stoping half way when the wind slows you down.

nothing better out there than a 182 for a family