Hi Markharf, thanks for your honest reply. I like that. Really.

About the wife: she was my pillion for many years and many thousands of kilometers, here in Europe. Our holiday planning was like this: "Where are we going this year?" one would ask, ,and the other would say "Well, why let us not ride around Spain this time? Or do you prefer the Italian Domolites? Or England?" and off we would go, just riding around and enjoying the scenery, looking for a place to sleep when the sun starts setting. That was before our daughter was born. We do it in a car now, or a small campervan (think Norway, and Bosnia and Montenegro) and we still don't know where we'll sleep. :-) So yes we like roadtrips and yes we like the unprepared and unexpected. And driving around in a SUV or other car with - f.ex. - a roof tent sounds very good to her. :-) As long as we can see and feel and hear and sense the country we're in, it's good for us.

About the daughter: well, there will be a day that she'll refuse to come with us, but for the moment she has to do with her roadtrip addicted parents. She would prefer 5*-hotels (with swimming pool!) and mini golf of course, like most girls prefer I suppose. But then again: she likes to camp and to sleep in a tent! So every year it's looking for that sweet spot between those two extremes.
Now, we hate being called "tourists", because we see ourselves more as visitors and travelers, and we mostly try to avoid the tourist traps. But alas, we know, we are tourists of course, though perhaps a rare breed, and now and then we visit those tourist traps because it really is too beautiful to miss out. But it wouldn't be the first time we didn't visit some castle or steam train because there were litteraly hundreds of people queueing!
About the emptiness of your country: it's without a doubt a stupid question. What did my friend tell me? 90% of the Canadians live within 100km of the American border?

About renting: so motorbikes are more expensive then cars? Good to know! Normally we rent the most cheap one we can get, like that Dacia (no airco!) in Morocco last year.

About the period: our daughters summer holiday is July and August, so we have no choice. May would have been better, I know, less hot and less tourists. But alas, it's something we can't change.

About cities: ehm, honestly, why should we want to visit cities?

Now, without kidding, this looks nice: https://thegreattrail.ca/ Perhaps this could serve as a lead, no?

Perhaps we should do this when we're older, without our daughter.... my wife almost jumped up and down with enthusiasm when she saw this: https://adventuremotorcycletravel.com/listing/trans-canada-adventure-trail-tcat/

Cross-border? Visit America? Hm, to visit the National Parks in the North West of the USA? Perhaps. Perhaps.

So thanks again for your advise, and if you've got more, just let it come ! I need this sort of discussions because they'll help materialize this adventure.
cheers,
Paul