There ya go - more on Cap Reef! :-)
Most National Parks - out in the western states at least - do not allow dogs on trails; basically limited to paved area like parking lots, etc. (Grand Canyon you can walk them on the paved sections of the Rim Trail though).
I do not know why you are not bringing your toad. IMHO you are severely limiting yourself in visiting some of the most spectacular areas in the U S. Even just trying to get into parking ares - pulloffs in particular - is going to be a real challenge, if not impossible, with the moho.
You are coming all this way and will miss so much because you are so limited.
I am sure you have a good reason - at least in your mind - not to bring it. And it may be very valid or only kinda.
If in the only kinda - bring the dogs and the toad. Then you can leave them in the moho (even crated if need be) and you will have the freedom to see God's beauty to the fullest.
See
www.LaurenBarbara.com and the Wanderings link and Utah and National Parks
We will be in Moab - Arches and Island In The Sky (north) section of Canyonlands, Capitol Reef and Bryce again this Fall for the colors. Not going to Zion.