Oh my! I can imagine your shock to see this guy/girl in your cat's house. Opossums are not cute to look at, it's true, but I find them rather fun and they are very useful since they eat slugs as well as rodents. It shouldn't harm your cat, your cat is more likely to harm the possum, but it won't like being cornered. You had better hope it isn't a mom looking for a nesting place!

You have created a wildlife friendly yard, and you have wildlife. The only way to stop this particular wildlife coming around is to remove the food. You could also use ammonia soaked rags, but I doubt if your cat will like that. Since they are good climbers, it's useless to try to place the cat house out of its way. The house actually looks far too exposed for a possum to really take over, they prefer more enclosed and tucked away spaces. I'll bet he/she was just curious and thought there might be food in there.

It looks like it's time to get Emmy used to being in your house if you are not willing to stop leaving out food.