Hi there! It's great that you are watching where your calories are coming from, but more importantly than being at 50% carb intake, it's the quality of carbs that matters. 50% calories in carbs from carbs such as vegetables, fruit, whole grains, and beans is perfectly okay - however, if all your carb calories are coming from sugar, bread, or other processed foods, that can be a problem while trying to lose weight.
Speaking from experience, (I've never had children, but I am also at the last 15-20 pounds and it gets harder) I never really "had" to exercise. I've lost 60 pounds since my highest weight, and the first 40 came off very easily, I did it all through diet. Nowadays, though, I've come to realize that my weight just simply won't budge unless I exercise.
I recently wrote a list of all the exercises I love to do, such as walking, hiking, tennis, sports, and jogging occasionally. I really try to only focus on those exercises. If I do something I actually enjoy, it's less like exercise and more like fun.
If you cut your calorie intake too low and don't exercise, your body can actually hang onto fat and make it harder to lose weight. Starving your body (for example, eating less tahn 1200 calories per day) releases cortisol (a stress hormone) that tells the body to hold onto fat. That's why it's important to eat a healthy, nutrient-rich diet and incorporate exercise that you actually enjoy.
I've only begun exercising regularly in the last month or so, and the weight is slowly starting to come off again (about a pound a month, but it's progress!) I think it's a longer process to lose those last few pounds, be patient and keep at it and you will do great!