Possums

I have a problem with some possoms in my backyard and don't know how to get them out of there. I also have 4 dogs and they have brought the possums already into my house. In the beginning I didn't realize what was lying on my carpet, it looked like my little boy Oskar at first until I saw that long tail...I screamed like a little girl and thank god I had a friend over that took the dead playing possom outside. I know it was playing dead because it was gone the next morning...
But that happened again and I do feel sorry for these poor little creatures. I know they are very slow and all they do is looking for food. I don't want my dogs attack them cause they can't even defend themselves but I don't understand why they don't stay away knowing there are dogs around. Are they that stupid or just hungry? I have an apple tree and that might be the reason for them to come around.

I'm from Germany and haven't even seen one of those animals before. Any idea how I can keep them away?