I think I understand what you are doing. You are planning to run the new drain under the new addition, under ground, and into the existing basement of the house where it will connect to the existing drain. This will likely be a 4 inch PVC line, at least it is at my house.
I had to do something similar for a 2 inch diameter sump pump connection. I rented an electric hammer drill, put a two inch diamond core bit on it, and went through the 8 inch thick concrete wall in about 1/2 an hour. For a four inch hole, it is likely to take at least an hour, but the process is the same. The hammer drill is pretty heavy, so make sure you get one with a stand. You don't want to be holding this device up for an hour. Also, make sure you rent a bit deep enough to get through your wall.
I had to do something similar for a 2 inch diameter sump pump connection. I rented an electric hammer drill, put a two inch diamond core bit on it, and went through the 8 inch thick concrete wall in about 1/2 an hour. For a four inch hole, it is likely to take at least an hour, but the process is the same. The hammer drill is pretty heavy, so make sure you get one with a stand. You don't want to be holding this device up for an hour. Also, make sure you rent a bit deep enough to get through your wall.