One problem is that she sees it as a hobby. It's literally life and death: Commuting by bike can cut cancer risk by half - BikeRadar

With little kids I suspect commuting time is the only exercise you get. So it's a big deal to stop doing it. Kids over 6 or 7 should easily be able to make cereal, peel a banana or (god forbid) toast a pop tart, and get themselves ready for school. If it takes 2 adults to get this done you're doing it wrong.

every time I'm tempted to offer spousal or parenting advice, I remember not to

What about the option of alternating riding and driving. Ride in one morning and the drive home and then drive in the next day and ride home. This wouldn't increase the number of rides, but let you ride more days. Perhaps, you could increase the length of the ride home to increase the total miles for the week.

There are several good options above too, but you and your spouse have to find what works.

Off point, but the final mile issue of not being able to ride, but it is ok to walk seems odd.

Also, consider looking into "travel reduction" or "commuter reduction program". Often if a business has a certain number of employees they can use these programs for their employees. I would think an industrial plant could benefit from being able to say they use environmentally friendly productions methods AND even use/encourage travel reduction amongst employees.
Sorry for the last part being a rant. It doesn't help with riding more, but it got me fired up. Maybe I should go for a ride. :)

Ask some women on advice. Both for dealing with it with your wife and for job bicycle restriction. BF is mostly male, from what I can tell. Understanding her angle, seeing how to make a win-win deal, or at least a decent compromise so no one is "damaged" (can't think of a better English word, sorry).

Do you have a slow cooker? You can use it to have breakfast ready when you all get up. Alton Brown has a great overnight oatmeal recipe, and there's probably ton of recipes at foodnetwork . com.

If that doesn't work, as stated above, be patient until the kids are older. HTH.