Merging 2 specific points
I've got an issue in Illustrator CC 2014 that's driving me completely crazy. I have tried e-ve-ry-thing for 2 hours straight for this ridiculously simple problem.
I've got these lines which are neatly joined together to form a single shape.

I then have to add in this last line.

But when I try to join it with the rest, it merges the wrong 2 points, like this:

I hope my explanation of the problem is clear enough. I have tried literally everything I could find on the internet but I can't find out why it does this.
Disclaimer: Yes, it is essential for my project to join those lines together.
Thanks in advance!