I also think Tusayan will be a better place if you want to see a bit of GCNP. Afaik dogs are not allowed in the GCNP lodges. Tusayan to ABQ already easily will take 7 hours just driving so I don't think you'll have the time for Meteor Crater (1-1.5 hours) or Petrified Forest (2 hours) if you want to stop along the rim first esp at Desert View.
There's a lot to see for R66 between Flagstaff and OKC but no time I'm afraid. Suggest to have something to eat at the cafe in Glenrio at the NM/Tx border and at least have a "mud" pie. Glenrio is the halfway point for R66 between Chicago and LA. In OKC don't miss the Memorial. No time for one of the greatest western museums ther Cowboy and Heritage Museum though.