Last night we got to drive to the hospital again. This time, though, as opposed to the previous trip, it was a lot more relaxed.
My wife started to have minor contractions around noon, which would slightly intensify towards the evening. By the time I got home from work, they would come in 5 minute intervals, which is a sure sign to get ready to leave for the hospital.
When we were there, she was attached to the monitor to quantify the contractions. The nurses told us they weren't strong enough, though (in their words: it needed to hurt more), so they were considered Braxton Hicks contractions (aka 'false labor' or 'practice contractions'). We were allowed to go home again.
It does mean we won't have to wait much longer for the actual birth.
Oh, and the nurses reassured me about not making it to the hospital in time: if my wife is about to deliver while we're still on our way, all I need to do is pull over, call an ambulance, and just 'catch the baby'. Very comforting...