Do you do in-home training? If yes, then this couple could become your best clients. With a 6mo old baby in the picture and with both of them wanting to lose weight, going to their home might be the best solution for them (and you). If she is self-conscious about her weight and image, training at home would take this issue out of the picture. It will also take the excuse of “it’s too far to the gym” or “I don’t have time” out of the picture as well. You can ask them if they would like to workout together sometime (or all the time), and this way they can have each other’s support. If she likes group classes, there are a couple of options. One, to join a group class at a gym and then train with you at home. The other option is to ask her if she has any friends who might want/like to workout and they can join her. Or you can offer a small group training for her and some of her friends (I like this option but only if she has friends who would like to join).
Having others who support people like your client might be the easiest and better solution to motivate someone who is sedentary. Another suggestion would be to ask her if she would like to sign up for a race. This could give her that extra motivation to start working out and stay with it. Losing weight is important, but the feeling and thought of training and working towards a visible goal (finishing the race) and accomplishing something that was thought to be impossible in the past can sometimes have some strong psychological effects.
I hope this helps.