Hi Synapse
After lurking for a while on the forum, I've registered so I can add to this thread.
I am, as it happens, a doctor but don't worry I work for the NHS here in the UK so this advice costs nothing. I have to be honest and say that I think what you are planning is a bad idea. Most of the replies you have received relate to distance but you are talking about 27 miles, 4 days a week which is clearly fine for anyone of reasonable fitness.
The main issue, as I think you know, is the timing. You are talking about a 3am start. You then work all day, have a quick nap on a bus and then have childcare responsibilities until your wife gets home at 7pm. Presumably you are planning on spending some time awake when she is home, so what time are you planning to go to bed - 9pm? That gives you about five and a half hours sleep before you need to get up at 2:30am. You are basically going to have the double problem of sleep deprivation and spending a significant portion of the night awake. There is increasing evidence about the health risks associated with night shift working - increased risk of heart disease, cancer and type 2 diabetes.
I really do think that what you are proposing will not be sustainable long term. Obviously it would be better for you to get a bus to work (assuming one is available in the early morning) and then cycle home but I assume from your posts that won't be possible due to the childcare issues.
I hate to say this, as I know how much I enjoy my own cycle commute, but perhaps right now your work and family situation aren't really suitable. Kids grow up really quickly, you know and very soon they won't need quite the help they do now, but they'll still want their dad to be fit and healthy.
Mike