As a 182 owner and only 182 experience my vote is against the 182 if the 1000nm trip would be anything other than a rarity with time to spare. Here are a few reasons against:
1. The Wife Will Be In Back: Although the back seat has a pretty good amount of room amongst all the 4-seaters, its still not exactly wide. There is a huge amount of leg room once the pilot and co-pilot are seated
However the seat is very low (think bent knees)
Most importantly, with your kids at these ages there is a 197% chance your wife will be in back with them instead of up front. She will have room but with a car seat she will feel like she's in the back of a Honda Civic with a lowered seat.
2. No way to have wife and both kids in back: No explanation needed. No way for all three in back of a 4 seater. I could see times at small ages where they might all want to be in back with mom.
3. Small Kids & 182 Panels: The panel in a 182 is very tall. Its my now 11yo daughter's number 1 complaint. Even with a 4" seat cushion its hard for her to see over the panel. Since I am guessing the older kid will usually be up front they will enjoy it but when it comes to flying it will be difficult for them until they probably reach 5ft tall. An adjustable seat would help but only so much.
4. Too Slow For 1000nm: I have some trips to about 500nm (one way). I think its fine for that. I've done one leg almost that long with a tailwind. With a headwind I know I would want to make a stop. Making any stop, especially with kids means like 1hr vs the theoretical 12minutes us guys think it will be. Once you add kids I think the 3hr mark can be pushing it. Unless of course they can pee while flying. I would bring those blue potty bag things with so my daughter knew she could go if she had to. Even had her try one at home first. That made her relax and she's never needed one. But 3hrs is a lot for a small kid. So you want that 3 hours to cover more than 450sm (which is fixed gear 182 speeds).
The OP has tons more flight experience than I will ever have and in way more types. So my only real question is can you afford that 1000nm trip?
Lets say you find a 150kt plane and fully loaded it burns 14gph. That is 13.3hrs of cruise and doesn't count climb outs, headwinds, diversions, etc. So lets say 16hrs of flight. That would be 2 x 8hr days. That equates to about $1300 of fuel. At a minimum you want to add in another $30/hr towards engine reserve so that's another $480 and how you are up to almost $1800. You'll most likely avoid ramp fees with fuel purchase but the one overnight each way will probably cost you $50/night for hangar and another $150/night for hotel rooms and food so now you are up to $2,200 for the trip. It would seem like a 170kt airplane can make this a one day trip with just one stop and cut several of the costs. But then again, higher costs.
I love the 206 - but just know there isn't a co-pilot door. Your little co-pilot or wife will have to crawl across the front or in from the bug huge side door (which is awesome).
You also mention not flying it when stationed away. When I was in the Navy I hated doing that just with my car. This might be a place where something like a 182 (fixed gear) is ideal. You could easily rent it out or have someone fly it about 50hrs per year for you. It will be just fine. Simple annuals and lot of people can fly it. And agree with the others. In almost all economies (other than total bust) a 182 seems to be in demand and pretty easy to sell if kept in decent shape. If your family ends up not liking trips beyond say 400nm just keep the 182 or similar low wing. If you are loving the travel, can afford it and want the comfort and speed you shouldn't be out much money and you can actually take your time to buy the bigger plane since the 182 should sell fast.
Probably most important. Have your wife sit in the back seat - that's where she will be sitting. That should help her justify the money on the bigger (6 seat plane) you want
If I knew I was going to do 1000nm trips once in a while and 500nm trips often I would want a TTx (1st) or SR22 (2nd) and I am a high winger!.