Last summer, my family and I drove from San Antonio to Alaska and back. It was simply unbelievable. Absolutely fantastic. The whole family enjoyed every day of it. My wife literally cried when we started leaving Alaska and heading back southeast. So, as you might guess, I'm a huge proponent of your doing this. Since I don't know your family, I can't really advise you on whether or not to have them on most of the trip vs fly them northwest. We were able to take a LOT of time going up and back (total of probably 100 days), and we were in a big motorhome towing our 100...so everyone had plenty of space and a toilet handy. Totally different setup that either your 100 or your pickup. BUT, if your wife and kids have the right perspective, it can be a marvelous bonding experience for all of you. My wife and I feel strongly that we'll look back on that trip as the #1 highlight of our entire lives.
Having said that, I think your schedule (21 days in total, if I'm not missing something) is overly aggressive. It's over 4,000 miles each way. Doing that in 21 days will be truly punishing on your family, no matter how hardy they are. There will be days on the Alaska Highway were you're going 45 mph all day....and you'll still be beating the heck out of your equipment. You won't make as many miles as you might think...unless you drive 12+ hours a day, which your family will likely grow to resent in just a few days.
Oh, and please do not waste your valuable time doing anything in the lower 48 on this trip. Spend absolutely as much time as you can in BC and Alaska. Given how far it is and what a time commitment it takes to get there...maximize your time in BC and Alaska. You can always do the west coast (OR, WA, and CA) another time. Trust me on this one.
Many people have asked my advice on taking a road trip to Alaska, and here's my suggestion for those with only two or three weeks of time. Fly the whole family up, yourself included, rent a Class C motorhome, and spend your three weeks touring up there. Just fly over everything from Houston to Alaska or the Yukon. We met a bunch of people last year who had done just that. There are tons of RV rental companies up there. Whitehorse, YT has a good RV rental business or two, as well as an international airport. In fact, every Sunday in the summer, there's a non-stop flight from Germany that comes in...loaded with tourists who do just what I'm describing. I talked with a few of them.
If you choose to drive your own vehicle, and if you have only 3 weeks, I'd highly recommend that you fly your wife and kids up to Calgary. Then, you and your dad could marathon-drive up to Calgary, pick them up there, drive to Banff, then take the Ice Fields Parkway to Jasper. Then, take the Yellowhead Highway west toward Prince Rupert, BC. Before you get to Prince Rupert (maybe 100 miles), take the Cassiar Highway north to Stewart, BC. It's easily the most spectacular place you'll see on the whole trip. Scenery was out of this world! Huge glaciers, tons of bears....just fantastic. It's as if the
Amazon and the Arctic collide right there. Hard to describe and unforgettable. Then get back on the Cassiar Hwy north to meet up with the Alcan. Then head west toward Ak. Keep in mind that when you get to Banff, you're still only half way to Ak. It's that far...
About which vehicle to take if you drive up yourself... For this trip, I would definitely take the pickup with the 5th wheel. I'm pretty sure the pickup would be more spacious inside, and you'll be super glad you have that 5th wheel when it's time to get some rest after driving 4,000 miles. Plus, once you get into BC, just about every night will be spent in bear country. I can tell you this - as many bears as we saw in some places, there's no way my wife would spend the night in anything without solid side walls. Plus, having the added comfort of heat (you'll need it every day up there), cooking capabilities, storage for fly rods and wading gear, your own shower and toilet, your own bed... if you have a 5h wheel, I'd definitely take it.
But one caveat... you WILL break stuff on that trailer. There's simply no way around that. Parts of the Alaska Highway are so rough that I saw people break axles, shocks, water tanks, windows, shades, plumbing, etc on their RVs and trailers. That's another reason to fly up and drive someone else's RV for two or three weeks.
I'll stop there. Needless to say, what you're planning is the ultimate trip in North America, and you and your kids will be eternally glad that you did it. I'm happy to answer any questions you may have, recommend RV parks, etc. I kept good notes.
Matt