A few things I'll share, as someone who has taken a decent amount of trips in the north east, and is finally getting back to it more regularly, and who has 2 young kids and 2 dogs (lab and small mixed).
You will not check the box with everything you want. You will need to decide what trade offs you're willing to make to best suit your needs here. There is no free lunch and all that. I didn't see if you mentioned about space, but if you're talking roughly 2-3 weeks a year worth of camping, and you have the space you can easily build out a used vehicle dedicated to your camping hobby. Something dedicated to the task at hand will always perform better than something you're having to make a bunch of trade offs for. There is also a potential that you can find a cheap-ish storage location for your camping truck/trailer. Again, all trade offs.
The other thing is the reality of camping with young kids. Since you've not done it yet I'll tell you it's not a picnic, and you've really got to want to do it to make it worthwhile for you. While there are a select few people who are willing to do whatever it takes to get out and camping a few times a year, the vast majority will not. Just keep in mind the desire vs reality as you're going down this road.
Ok, so you've decided that you want to camp, and you want a single rig that is a daily as well as a dedicated camp rig. You've also decided that you want a cap/campershell combo. Great. Firstly, it's gonna be hard with a single young kiddo, and even harder with 2. As they get older you're gonna find yourself exceptionally limited on space. Plan for bringing some sort of large tent as additional "out of truck" room for hanging out in or sleeping.
As for rigs, you can't do a midsize rig. Well, I suppose you could, but you're not gaining anything really. I'd look at full size, and frankly I'd look mostly at the Ram 2500 platform. Reasons:
- Turning radius of the Ram HD is shorter than the new Tundra, F-150 and Silverado, it's slightly larger than most midsize trucks by about 2-3'. I've not yet found a trail where I can't do a little wiggle to get around, and I'm in the north east, where it's pretty tight vs the west/southwest.
- Payload is far higher than any of the other 1500 series trucks, and the frame, steering, etc. are all far beefier stock. That is going to mean longer life out of your components.
- Pretty solid aftermarket support. Not as much as jeeps or tacos, but prob better than F150s and def better than the silverados
- Current Ram HD trucks are the same design, frame, suspension, cab, etc. as they have been since ~2014. That means more parts availability.
- Hemi or Cummins engines, both get good to fair MPG, and both are solid engines at this point.
I would personally avoid the 1500 series trucks for the reasons listed above, plus for the slightly increased cost you get something much more stout with the HD platform.
As far as others recommending trailers. Yeah, it's not ideal. That said, you said two things, you like to go deep into the woods for 10 days at a time, and you like to explore cities. Well, which is your focus? If you want a better "camp" experience, the trailer is hard to beat, especially if you are able to drop it off for a few days to explore. (eg. find a campsite on the outskirts of seattle, drop the trailer and enjoy a few days exploring the city, enjoying showers at the campsite, then get back on the road out into the bush)
FWIW, I went through a similar process a while back and landed on a Cummins 2500. I wouldn't recommend the Cummins engine unless you really wanted the extended range or were just a diesel bro (me on both counts), but it's an option. I initially was towing our 32' trailer with it, but we have since upgraded to a large 44' toyhualer with necessitated a dually. I've been blessed with the income and job that enable me to do that style travel so we plan to take full advantage of it.
I did fall in love with my 2500 though, so I've kept it as my daily/camp truck. Thus far, I've been able to slap on a cap, front and rear bumpers, winch, etc. and continue building it out for trips "with the boys" and eventually with the kiddos as they get a bit older. It's vastly overkill for my needs, but I love the damn thing so I'll own it till it rusts apart most likely.
