OK I am not sure what is up with the assembly or if it is from the new update patch we just had but I am geting strange reactions from alibre while working on this, I also had some odd issues with a project of my own after updating so I am not sure...
OK back to your question. Since I can't show you I will try and explain what I would do ....
First get rid of all your current assembly constraints. Now constrain the outside edges of the parts that make contact that would be three constraints, the two base part edges constrained to the outer parts edge, and then the two outer part edges mated together. This will put all the parts in just the right place.
Second edit the base part. One of the mated edges is perpendicular to a plane so select that plane and create a new sketch. now select project to sketch and select the two faces of the adjoining parts (you may have to hit the orient to plane to flip the view) ok. now you will have the two sides profiles drown in your sketch, delete all the outer lines leaving only the diamond in the middle, this is where the two parts intersect. There should be four sides to this draw a line from the outer tip to the inner intersection, and delete the two lines that you don'[t need, this leave the part you want to remove, do an extrude cut "through all". NOw save and edit the other part in the same manner.
Now on all the other edges you do the same except you will first need to select an edge and right click on it and choose create plane, to add a plane perpendicular to the edge.
I hope that helps and you can understand what I mean.
Don't beat yourself up just say cool I now have two ways to do it. And getting your work flow down takes a bit of time, one tip though that would have saved me allot of time is use sub assemblies because when there is a problem it is allot easier to fix small assemblies rather than one large assembly.