Ick. Are the dogs new? Or is this something that has been going on for a long time and your mother is unconcerned about it? Are the dogs old and incontinent? Does your mom clean up the messes as they occur?
I just can't see how your mother, in her right mind (and I say that sincerely- as she might be developing judgment issues due to age) would not understand that it is unsanitary and not a healthy environment, either for a child or for her and your grandmother. You didn't say how old your daughter is, but I am assuming that she is school age and not a toddler.
You MAY be able to "soften" the blow by saying that you are aware that SHE doesn't have an issue with it, but that you have chosen to hold your daughter to a higher standard and don't want her receiving mixed messages. I doubt it will make much difference how you word it. Either she will be offended due to low self-esteem, or she will choose to ignore your comments in the same way she ignores the deplorable condition she allows her home to stay in.
Perhaps a loan of a dog training book might be in order?