I don't know about Canada, but in the US technically your drivers license has to have your current address (you only have something like a few weeks to change it) -- I haven't changed it in about 8 years as I've moved in and out of the country, and it's only come up a couple times (because it wasn't consistent with my address written on other documents), but it's never been too serious. You may want to check on policies there, and for other cards - billing addresses, health care, other ID cards, whatever - and also possibly where you want your mail sent (it could be the old address and then be forwarded) or where you're officially a resident or registered to vote (if those systems are similar).
I recommend that when you leave the country you pick a Canadian address to use and put that on everything. It could still be your old house (for a reasonably short period of time), as long as you're forwarding your mail somewhere. Or you could change it to your grandmother's if you think that will be useful as a 'home base' for a significant period of time. There have been times when I've left the country that I've used different addresses for different things and it got much more confusing than just always using one (like my previous one, even if it wasn't actually valid any more).