The pet industry have pet day care centres, pet overnight accommodations but no one seems to cater for those after work emergencies/engagements. My neighbours often ask me to walk their dogs when they couldn't and pet/house sit while they are away. I can visit once a day or stay overnight depending on the dog's needs.
I work office hours at the moment but I am more than happy to look after your pets after 6 pm or on the weekends....