I have felt like your wife is feeling, and I only have one child. I remember calling H in tears and asking him to come home or take a day off, too. Parenting is so stressful, and being a SAHM is tough. Showing her empathy is the right thing to do. Since this seems to be her reason for leaving......curious.....have you or her ever suggested she work parttime and put them in daycare parttime. Some moms are better moms when they are working in a job outside of the home.
A friend recently talked to me about the fact that when I left my fulltime job to stay home with the kids I lost a lot of recognition and appreciation that I got with my job. I started expecting even more of my needs to be met by my husband. I am realizing that my H can't be everything for me. It could be one reason why I looked for something outside of the marriage to validate me instead. Also, does she have some SAHM friends or a network. I know there are also lots of mother of twins groups. Twins have special challenges that onesies don't. Just wondering if she has some kind of support system other than you for that. ....thinking out loud I guess.........