I'm thinking of hiring a plumber with a camera scope to find the connection and then I'll dig it up and plug it. Is there any reason it should be this way???:

(I wonder if it could be a secondary way to protect the basement in case the pump fails???)
If the pump fails it will be the primary source of your trouble
You probably wont find any one connection, just finding it's way under footing. An out side system should only be used with a gravity daylight exit drain. Never in combination with an inside system for just the exact reason you discovered. You should at least disconnect the roof leaders from that system, if you can't isolate the exterior system from the interior.
If there is no way to have a daylight exit drain then no system should be installed on the outside. An interior footing drain should always be installed regardless of if there will be one on the outside or not, easy to do for new construction, expensive to do on existing.
Just witnessed the same thing your describing at the house I worked on last Monday, I worked on the existing basement but they were putting an addition on the back of the house, the contractor put a sump pit in the inside with an interior perforated footing pipe (the white PVC type with holes just on the bottom, First mistake) then they put the same system on the outside.
This is a small lot with no way to have a gravity drain, they bedded the outside system in tons of crushed stone, I questioned the builder as to where the outside system would drain and the answer he got from the foundation guy was not clear at the time. When I came back last week they installed another sump pit on the outside, 7 ft deep!!! future nightmares. I don't care, more work for me in the future.
Ideally in that situation you damp proof the walls and back fill with just dirt compacting as you go, this way you hold as much water back as you can with compressed earth and monolithic concrete foundation, any water that does get by will be controlled by the interior system. with all that stone you are collecting ground water in a huge reservoir on the outside of the foundation. In this case they will have to run a pump in the outside pit or all that water will come through to the inside system, either way they will be pumping more water than is necessary.
This is an area of construction that is not well understood, there is alot of debate over the right way to do it, we often see builders sabotaging themselves with stubborn ways of thinking.
Again, more work for me so I've got no problem with it
JB.