Yeah. I've tried the use key repeatedly as both myself and the mouse droid. Believe me... the poor use key is just about worn out.
I did solve the problem after many *many* frustrating reloads/replays last night.
I rolled the mouse up to the big door.
Opened the door.
Shoved/kicked the mouse inside. (The mouse didn't enjoy this treatment, and I took a little damage from the radiation to boot!)
Went back to the control room.
Finished the level.
Strangely, once it was inside that room, I had no problems with the other droid ports. After flipping all of them, I went back to that door from the other side, and it opened no problem. So I thought I would try to open it again from the side I was having problems with. I discovered after still more persistence that it *will* work, but I have to be at less than a 45 degree angle to the left corner for it to work. Going at it straight on or to the left or right a bit will *not* work. And it still wouldn't work being at an angle on my previous saves. So my install is bad. I can hardly wait to see what fun comes next.
Oh, and in the briefing with Mon Mothma for the second mission, Kyles face is on the inside-back of his skull, and the front of his face is transparent, except for his moustache and two black eye holes that blink. Funky!
ps: Netrunner, the droid you're thinking of is a Power Droid, and that's the mining level right after this part. I couldn't get him in there either, so I gave up. After the problems I had with the stupid mouse... I was ready to find another alternative. Since I finished the level without figuring it out, I didn't bother going back to unlock the mystery.