My mother and I temporarily lived in a place (about 5 days). After we moved out, she said she woke up and saw a packrat tugging at my hair. She didn't tell me because she didn't want me to freak out. (I was in my late twenties - we had gotten together for "grand adventures, which we had.) Lest anyone freak out, I need to point out that the house was in the country, had not been lived in, and was far from finished. It also had a skunk that would come in at night. I heard it and went into the bathroom. It was in the bathtub and was not happy about me being in its house.
Cats and, I understand, rat terriers are good animals to have around. Because cats are not friendly to their prey, rodents learn to stay away from areas where cat smell is.
I would leave a small light on in the bathroom at night. If it freaks you or your children out to think of a rat/mouse in the toilet, perhaps you could keep a stick there to rap on the lid before you open it (assuming you keep the top lid closed).