Yeah the GT350 makes the most since, considering he does cross country road trips and uses the GT350 as a daily driver. With the GT350R you have to worry about your splitter and the carbon fiber wheels. You could install the seats and get the insurance or swap out the wheels but by then you would have already invested even more money into the car on top of price of the initial sale. The GT350R is just more hardcore, the GT350 has the perfect balance of being hardcore but still being practical (As OP already knows, otherwise he probably would not daily his GT350).I'm surprised you can get that high of an offer with that many miles on it and having used it like you do (driving in snow/salt etc.). I would probably either keep driving the car as is or take the trade.
Personally I would trade for a newer/low miles GT350. I'd find one with a long warranty and keep using it the same way you have been. The regular GT350 is the one that's intended to be used the way you want to use it. Everything the R has over the regular GT350 is geared toward making it great on track and many of those things could make it a little less enjoyable on the street. And I've been around this forum for a while - I don't think you are a track guy or if you are you sure don't talk about it.
For a cool climate the heated seats are awesome. The R doesn't get those IIRC.
The GT350 has more comfortable suspension settings. I think it is perfect for commuting. Firm and controlled, but almost never too firm.
The regular GT350 wheels are relatively inexpensive and even though you have money you don't seem to ever want to waste it. The carbon fiber wheels costs thousands each to replace. You can get insurance coverage for them, but that is costly as well. The CF wheels have the reputation of being amazing, but I don't think they are worth the extra money for your use case.
The lower ride height and big splitter on the R are going to be annoying at times for both you and your wife. Sure you can think of it as fun trying to figure out how to get where you're going without scraping, but it's enough on the regular GT350. The R is quite a bit lower. I would personally avoid it, especially for winter driving where you are essentially going to be driving a snow plow on some days.
And your 10 YO won't be riding in the back seat of the R. Reason enough IMO. You won't be able to drive it whenever you need to drive the 10 YO somewhere. Means it will be parked more of the time and just in your way.
The R is amazing - I'm not cutting it down at all. But for what you want - the regular GT350 is a much better choice IMO.
It would be better to get a GT350 and then just by the red pinstriped vinyl, red badges and the CF wing vs getting a GT350R and getting new rims/rim insurance, and adding rear seats (Its not easy to get that done, the kit isn't available and you need to find someone who is willing to give up their seats with a GT350 or find some online)
Ford already thought of this, which is why there is the GT350 and GT350R