Deleting the corresponding entries from the second table when you delete a dog from the first is definitely possible. You would just have an additional delete record server behavior and specify to delete from your second table where the deleted dog id matches the picture_dog_id. You can also use the delete files server behavior to delete the corresponding images as well.
To prevent the dog record from being deleted if there are entries in the other table you would have to do a custom check by having a recordset that selects all from the second table where the id matches for the first table. If there are any records in this recordset it would indicate that there are corresponding records. You could then redirect and display an error message.
Please post back with any specific questions that you have about any part of this.
