I have to wonder why on earth you'd ever want to be skinny?? The friends I have who are skinny (just naturally) lament their figures regularly.
First make sure that you're shooting for a healthy and realistic weight. Then realize: 125 lbs after 2 kids isn't going to look like 125 lbs did in high school!
I'm 5'5, and my weight is between 125-130, depending on how much PMS water I'm retaining. With the exercise, make sure you're getting both aerobic exercise and strength training. Not only do you need both for healthy weight loss, but for your health in general. The aerobic exercise helps your heart and vascular systems, and the strength training helps keep your bones strong.
The first thing to bear in mind when eating is portions. We eat TOO much at one sitting. I'm sure you've heard the 'small, frequent meals' recommendation, and it's true. I have breakfast after I run in the morning (oatmeal or grits and skim milk, usually, or maybe cheerios); breakfast #2 a couple hours later (yogurt smoothie with blueberries, bananas, strawberries...and maybe a handful of nuts or something salty); lunch -- could be half a sandwich (I use spinach in place of lettuce on my sandwiches), or soup and peanut butter crackers, a big salad (gotta have some kind of protein on it though or you'll be starving soon), then in the afternoon a snack with a veggie (celery and cream cheese, carrots and cream cheese dip), and then dinners. We make all kinds of stuff for dinner, from healthy to fat-laden but totally yummy to pancakes to mac and cheese. If I eat regularly through the day, I'm not starved by dinner, so I can have a reasonable portion of absolutely anything, including a little dessert. I have not denied myself any 'kind' of food -- I just eat a reasonable amount of it.
I know lots of people swear by Weight Watchers, or other eating plans and 'diets'. I think, personally, it's all crazy. If you are exercising sufficiently, and eating intelligently, the way our bodies are made, it is impossible to be overweight (unless you have an underlying medical condition or are taking medications which cause weight gain). Our bodies are very simple machines in this way: energy in, energy out.
It's absolutely key to drink at a minimum 64 oz of water a day. I drink about 90+ ounces, just sipping all day, not even trying to hit the 64 mark. It helps with the water weight and flushes toxins out.
When my son was born, I weighed 193 lbs and dropped to about 145 before my daughter came along. By the time she was born I weighed 198. I understand how hard it is to lose weight. Have some patience and mercy for yourself: you didn't get there overnight, it's going to take time (a pound a week). But -- as you get healthier, you won't have those cravings for junk foods. As you hydrate your body, you won't mistake thirst for hunger. Your body will want lots of water and healthy stuff. You'll re-learn your body's cues for being full (when you think you're just starting to get full, sit back from the table for 5 minutes. I can almost guarantee you won't just be 'starting' to be full, you'll BE full....but your mouth will want to keep tasting. It's really interesting how we've learned to eat...)
Anyway, enough of me rambling. Just remember to be healthy. Skinny isn't the goal; most of us aren't built to be twigs, especially after childbirth. Treat your body right!