Actually you can lose A LOT of weight with walking being the only exercise. Any thing that ups your heart rate is going to burn calories. Exercise is only a small part of the weight loss problem. How is your diet? What are her portion sizes like?
As for the fact that she doesn't like her post-baby body, that is completely normal. Since I had my son (he is nearly 7 now) I will still often break down and cry at the 'horror' that is my body (only when I am PMSing these days though).
I'm sorry for my callus attitude, but FFS, suck it up!!! At least you are getting something at the moment. It's only been in the last 2 years that I got any of my sex drive back. For the rest of that time I only ever felt like doing anything maybe once every 6 months. Hubby 'got some' maybe once every 2 months out of a sense of 'obligation' to him.
There are plenty of women on the planet that go completely off sex for a LOOOOONG period of time after having a baby. Some women never get their drive and self esteem back. Be thankful that she does want to change.
Stop mentioning the gym, start recommending healthier eating options and smaller portions and go for an hour long walk with her and your baby once a day. Oh and make sure you give her some time to herself everyday too. Being a mum is hard work and draining, after giving all her energy to your son, are you surprised she has none for you or herself.
'People are never perfect but love can be. People waste time looking for the perfect lover rather than creating the perfect love' - Princess Leigh-Cheri from Still Life With Woodpecker.