I'd just start knocking out the project backlog and see how things go. See which projects you enjoy, and think about which ones you enjoyed and think you could make money at. Once you go out and get a part-time job, you can very quickly lose the flexibility to pick up sick kids, go on their field trips, etc. As much as possible, I'd try to work for yourself in something where you could have a flexible work schedule to accommodate the needs of your family.
First, I'd get stuff organized that I've never made time to. I'd have the basement/garage of my house whipped into shape so I could actually find stuff easily (including tools). I'd then organize the room that could be my office if it were not in complete shambles.
After that, there are dozens of little and big repairs I could make around the house. Some are as small as touching up paint. Some are much more involved.
In all honesty, it sounds a lot like what my grandfathers did when they retired, except they didn't do that plus take care of children at other times.
I would personally spend her money on my car projects, but since you are a beautifully enlightened person who wishes to give back, here is what I would do:
1- volunteer for a charity; a soup kitchen, a volunteer fire department, meals on wheels, or a local kids' shelter coaching [insert sport here] about which you know. Your time commitment to those organizations affords you much easier "emergency time off" if you need to take a kid to the orthodontist
2- Hit up your local YMCA and see if you can offer classes on whatever it is you do best.
3- This will sound odd (but those of you who know me will understand) - Meditate. Focus your energies on healing and prosperity. Don't supplicate, manifest.
I'd teach my wife to think like yours. 
No wait...that wouldn't work. 
I'd spend more time a the range.
God, I need a wife.
I been pretty lucky in life... think I would volunteer.
Nano brewery. 
If I were in your shoes I'd go back to school.
Great position to be in. So much to do... I am 100% disabled with a spine that is completely shot, along with severe arthritis in my hands and other problems. I maintain the house, and 1 acre of yard, take care of the kids (all have 4 legs here), do the cooking, continue to upgrade my race car, and learn new things via History Channel and the great variety of PBS channels on our cable lineup.
I miss going to work every day though...
Lesley wrote: God, I need a wife.
My wife and I want a threesome. No, not that 
We want a third person to do all the work around here.
I'd go backwards.
I'd refocus on some things I used to have:
Spend a lot of time volunteering with Habitat for Humanity and other non-profits.
Spend more time with kids (mine and others), including coaching, teaching, and mentoring.
Spend a little bit more time on projects- cars, house, etc.
Daily quiet time- slow breakfasts, read newspaper, prayer and meditation.
Spend more time with my wife.
Travel- missions trips, etc.
Maybe some continuing education.
That used to be my entire life. I've traded an awful lot of it for a paycheck.
Serious answer:
Bye honey, see you in 9mos... tell the kids I'll call from the road.
RG1150 + hard bags and a ride to the southern tip of south america, pausing to climb Orizaba / Iztaccihuatl in MX and Cotopaxi & Chimborazo in Ecuador. Whatever else comes to mind along the way.
I have 20yrs of overtime to "get back".
There will still be plenty of work to do with the kids. If you find you have idle time, your local sports car club probably has some volunteer labor that needs to be done if the spare time presents itself. Promoting their events on the web, putting up posters, organizing the club trailer and so on.
My winter schedule means I have my one or two days off during mid week. My son just started public school, two days a week half days. In a year or two he'll be full time. I'm eagerly looking forward to having some free time during the day to get stuff done around the house. You don't realize how much time you use to have until you have a few minutes to get stuff done without the help of a toddler. I'll miss spending that extra time with him, but I'll have to be productive or I'll go nuts.
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