The fastest route from Sarnia would be through the US. Did you not want to do that?
If not, then #17 is probably best. You can google map the route... how many hours a day did you want to drive?
I'm google mapping it from the Soo (friends there we can stay with the 1st night) So yes would drive thru the states to get to the Soo. So from there to Drumheller it says 26 hrs Canada way or 27 hrs US way (not much difference in time?) Probably 10 hrs a day of driving? Plus stops. Aiming for the best route for our dog, with picnic areas to stretch, pee, etc.
this is a good site for where to stay with a pet http://www.petfriendly.ca/
and when you look up the time of travel on google maps it is for wheels turning - 4-5 hrs if you are sight seeing 6-8 hrs to get somewhere and 9+ if you really want to get there (-:
this is a US route https://goo.gl/maps/267M1hiu6c12
and via #17 https://goo.gl/maps/mw922QoEpRT2
Yeah ... you neglected to mention the Soo part in your initial post.
It's really up to you ... there isn't a lot of difference time wise. Perhaps go out one way, come back the other.
If you really want to push it, you could do this:
With the dog, you'll likely need to stay in larger towns/cities - more accommodation options. As for rest stops, pull-outs, etc., there are plenty along the way. The drive from SSM to Thunder Bay is quite spectacular, so you'll want some extra time to stop on that leg. Also, driving at dusk & night through northern Ontario can be dangerous due to animals on the road. Thus stop in TBay, get a good rest and an early start the next morning.Edited: 10 May 2018, 05:20
Thanks! I think the Soo - Thunder Bay - Brandon - Drumheller (& on) looks great, yes more time for the Thunder Bay part. And yes more pet friendly hotel options in TB. I found this site good too https://ca.hotels.com as I can select pet friendly - it gave me way more hotels then the http://www.petfriendly.ca/ - go figure! ;)
You'll need the proper documentation on your dog crossing the US border. Proof it as had it's shots, etc.