Your wife is a stay at home mom with two pre-schoolers. She is now a mother 24/7. She needs help in breaking out of that 24/7 part of the mom equation.
I'd suggest that she join a couple of weekly workout groups at the YMCA. My Y has maybe 20 classes a week and some of the women have been attending the same workout class together for years. Women love these things... something about the social/herd mentality of women or whatever. Regardless, they get addicted to the classes.
I've gone with my gal friends and was blown away by how tough the workouts were. She'll make new friends and more important, develop some new role models rather than the fatties she's meeting in her charitable work. (Sorry to be blunt, but with 67% of the population overweight, the only non-fatties are adults who make exercise a priority in their lives. Right now, that's not your wife.)
Oh, and add CrossFit to that weekly routine if you can afford it. For all the grief we give CrossFit here, it's fun and can be addictive if you get in a good group.
Bottom line: She needs more personal time away from the kids and ideally should spend that time in some sort of high intensity exercise class. The nutrition should adjust itself once she starts hanging out with fit, athletic peers who are having fun exercising together.