If you have the petsafe door already working with SmartThings, you should be able to do this quite easily with core, which allows for a “while” condition
CoRE (now WebCore) is a very powerful community – created rules engine for SmartThings. It allows you to set up stacked conditionals like “If A then B but only while C and not if D.”
Setting it up can be quite complex, but there are many community members who will be glad to help you.
For example, here is a piston that one member created to notify him if the dog had already been fed twice that day and he picked up the dog bowl for a third time. He needed this because he has a large family and people didn’t always remember whose turn it was to feed the dog.