I have six dogs and I would NEVER take them into someone else's home just out of fear they would have an accident.
Does Trudy have pets? Then the answer is: my pets do not do well around other animals in their territory so you will not be able to bring your pets anymore.
If Trudy does not have pets: I don't own pets because I don't want the smell, dander, mess, shedding, therefore please don't bring your pets to my home anymore.
The reality is, even if they don't mess, they shed, have odors and dander, etc and this is left behind when they leave.