Confused, you sound as though you don't have much support.
DH expects meals served to him, although you work full time as well.
DM is just harping on about you losing weight, without being in a position to provide practical solutions (either by giving help, or practical advice).
From what you have posted, this isn't just "baby weight" that needs shifting.
So, you need to speak to DH about giving you a chance to do some exercise (make sure you get to go for that walk at least every other day, while he prepares a meal that doesn't need cooking like cold chicken and salad) and get some support to lose some weight (lots of threads on MN, online Weight Watchers, that kind of thing).
And speak to DM, if you can. Without being stroppy, can you tell her you could really do with her support, that you would like to lose weight, and are finding it difficult, that you feel a bit snowed under by your situation, working full time, and having a little baby, and that her nagging you is just adding to your stress? Perhaps a letter or an email would be good. (If you don't think this will come off, you may just have to learn to tune her out.)
And remember, it is perfectly possible to be both fat and fit. It is perfectly possible to be thin and unfit. Healthy is the goal, not thin.