You certainly will have no trouble filling your time! There are many places you are missing, and of necessity must be missing for the area you're covering, so there's no need to worry about that. I certainly understand the difficulty in spending lots of time away with family and work schedules, and I myself often cram a lot into trips; but trying to see even all the highlights of the cities you mention in a day or two is questionable. With the time constraints, I would prefer to see just one or two things decently well than have a big checklist scavenger hunt to see how many recognizable things one can somehow get to.
Philly, besides the historic sites, has a lot of other cultural sites, such as the world-class art institute (a huge museum) and the academy of music.
For NYC, it may be worth looking into a packaged tour as you can spend/waste a lot of time trying to figure out how to get from one place to another if you aren't familiar with the area, and more time waiting in line for tickets etc. I might consider catching a Broadway (or off-Broadway) show, besides the things you've mentioned; and, if the weather is clear, go to the observation deck on the Empire State Building. There are an enormous number of museums as well, some well-known and some lesser known.
Whale watching at Cape Cod would be a full day, particularly by the time you get there and back. The New England Aquarium is a good half-day activity in Boston; the Science Museum is also quite good and has a very impressive van de graff generator show. Avoid driving in Boston (even without the camper); driving under the city when it isn't rush hour is not too bad, though propane is not allowed in the tunnels so that would presumably have to be without the camper.
The Cog Railway up Mt Washington is one fun thing to do in the White Mountains. There are some very pretty roads through there, too; I'm partial to the Kancamagus Highway, which has quite a few opportunities for short and not-so-short hikes along it (most of which can accommodate at least a few RVs in the pull-offs).
The chances of seeing the Northern lights where you'll be is quite slim, and longer summer days don't help things any. You really need to get a good bit further north to have much of any reasonable expectation of seeing them, and the middle of the summer has even less light at those latitudes. That's not to say that you might maybe get really lucky...just don't get your hopes up.
Crossing the border into Canada is not generally difficult, and usually in my experience does not involve too much delay, though that can be variable. The officials I've encountered have all been professional. You do of course want to make sure you have the appropriate paperwork (passports or equivalent border documents, or a birth certificate is sufficient for the children last I checked).
Gas and many groceries are a little more expensive in Canada, but it's not a vast difference in the grand scheme of things...maybe something like half again more for gas, if that, once you account for converting volumes and currencies.
If you went to the White Mountains before Acadia (or skipped them altogether, or skipped some other things), you could maybe head up to Quebec City, which is a fascinating place.