I've been looking at the Data book for alternatives to the Rincon mountain pass.
There is only two other mountain passes that I cross on this segment of the trail. The first is at the very beginning, the Huachuca Mountains Dec. 13-Dec. 15. These are in the Coronado National Park which allows dogs in area limited areas of the park. I'm pretty sure that the section that I'd planned on doing is dog friendly, but I could find any empirical evidence. A phone call to them would probably be best. (520) 388-8300
The second mountain pass is over the Rincon mountains which, I believe, are in the Wilderness of Rock trail jct. I propose you join me for that one and meet me somewhere Tucson and hike to the end with me. That would be 4 days and, depending on where you meet me, 47 miles. Pretty big days I know.
Let me know the your thoughts on what I have here, and we can talk more about details if it is feasible for you to do this section with me. Look forward to hearing from you.
All the best
"Brothers. What we do in life, echos in eternity."
-Maximus Decimus Meridius