OK -- this is gonna sound corny -- but I'm gonna say it anyway.
Animals understand death -- but they do not understand disappearance. If there is any way that Cheyenne could be allowed to see Patch, it would help her. If Patch is not available to her, then explain to Cheyenne what happened. Out loud, and in the language you would use for a child. I think it would astound us if we knew how much they actually understand.
For what it's worth.