Not that you want to do this during bloom season, but you can cut the foliage back almost to the ground, and spray what is left with a 5% Dawn solution. (I have also tried Chlorox cleaner with bleach, which is a commercial kitchen type cleanser that comes in a spray bottle; it did not harm the plants.) This approach will give you relief for a little while, and should be pet safe. (The Dawn certainly should be; I'm not sure about the Chlorox, but I would think that any pets would avoid anything smelling of bleach.)
I did both of these things this spring, when the rust was spreading everywhere. Plants that looked absolutely horrid grew back in green and clean, but some of them get hit by irrigation and so (possibly because I did not treat every single plant in the garden) the rust may be starting to reappear in places.
Good luck to you; rust is a scourge.
