I'm not sure if you are this way, but it sounds like this is more for you than her. Again, i may be wrong, but all the "i got a great metabolism" and "she doesn't want to join the forum" and "shes not a fitness freak" sounds a little suspect to me. No offense, i just call it like i see it. Its fine if you want her back in shape too, but you gotta be mindful of the most important priorities. Your wife's mental health and your child's physical health.
So here's my advice as my wife just delivered our son back in October and has lost over 40lbs and is back to her pre-pregancy weight.
1. I wouldn't have her eating a crazy, super strict diet if she is breast feeding. She can eat clean, like MM posted, but i wouldn't go overboard. She has to provide all the nutrients she can to your baby, and eating super clean isn't necessarily the best answer. I agree with Blondie, her doc should've told her what is good. Military or not. I was in the military and you just gotta know how to ask. lol Anyway, things like diary aren't always great when it comes to losing fat and getting back into shape, but they are great for a breast-feeding child. Right now the kid is more important.
2. Have her drink at least a gallon of water everyday. She's gonna be home alone with the kid, and she won't wanna pee all day long, but water has been shown to be a great regulator of hormonal imbalance, which is what all women go through after the have a baby and one of the biggest contributing factors in regard to weight gain, loss, mental health, etc.
3. Tell that woman how fucking hot she is everday. I don't care if you think she knows or she disagrees and tells you to shut up. Make sure she understands that she is the hottest woman on Earth... and mean it. If she thiks all you care about is her getting back into shape, she's gonna think you think she's fat (which she already thinks she is anyway) and things will be worse. And just cause she is a stay at home Mom, she doesn't have to feel that way. If its the weekend and you wanna relax cuz you been hard at work all week 'bringing home the bacon", fuck that. Tell her you'll take the baby on Saturday and send her to get her hair and nails done. Make dinner for her one night. Or every night. See if Grandma will come over and watch the kid for a few hours and you two go rent a hotel room and just make that woman writhe in ecstasy for the day (if its soon enough for her to have sex of course).
Again, not saying you aren't doing these things, but lemme tell you that the amount of respect i have for my wife increases by a gazillion once i saw her deliver my son. I have never been the same. And like most women she thought she was fat, ugly, etc afterwards, like they all do. So i made it my purpose in life to make things as easy as possible for her everyday. I did the laundry, dishes, cleaned the house, changed diapers, washed cars, whatever it took. I even took off two months from the gym when she was able to start working out again cause my son was too small for the daycare. And she told me it made a huge difference.
Just another approach cause it sounds like shes doing great. And again, not trying to be a dick, just hope this isn't more for you than her.
One more thing, you mentioned she can't leave the house. How long ago was the baby born, and do you not have any day care options?