Yes, UA might cancel the second booking (or both). You could try booking with or without your middle name and leave your MileagePlus number off the booking (and add it back later) then when you get to IAH ask United to cancel the last segment. Obviously you can't have luggage in this situation either. It's still very chancy in theory they should match your birthdate and name but who knows what goes on in the bowels of the IT booking system; I have never done this. I HAVE had to do the step off the plane in LAX and cancel a second segment on the way back from Hawaii one time and go to Baltimore instead of back to Toronto, but it was separate airlines (transferring from American to Southwest - not fun at LAX).
You could also look at another airline with a stop, but that will also take longer and may be a waste depending on how many FF programs you participate in.