A stone (and a half) is not a huge amount, you might feel like you have a mountain to climb but it's doable, don't despair or cry 
you say you have been trying to eat healthily, what does trying entail? I, to my great suprise, have lost 9 lbs in one month using MyFitnessPal - I've eaten all the calories it allows me per day based on a target of 1lb a week (one or 2 slip ups along the way). I haven't felt at all deprived, I still eat delicious food, still eat out a lot, still ate cake on four birthdays... Tracking my food online has just made me more conscious of what I am shovelling in my mouth, and makes me sort of bargain with myself. if you are just"trying" to eat healthily, it is easy to lie to yourself and pretend that your portions are reasonable and pretend the slab of chocolate or bag of percy pigs you inhale on the move doesn't count. I find measuring, weighing and recording my food has changed the game completely. It really isn't that much effort.
People worry that calorie counting can make you obsessive, it can but if you approach it sensibly it is fine. I used to have issues with food abd have been encouraged not to diet (even though for health reasons losing a couple of stone was drastically needed) but once I finally decided to take control and responsibility for my diet and not consider its impact on others, I felt more relaxed. I understand that you don't want your children to have issues, but that is more likely if they have a mother who hates her body. they don't need to know what extent your dieting goes to, and anyway it is important that children learn about eating for fuel, eating healthy and sensible portion sizes - that kind of thing is very difficult to adopt as an adult. You can use them as motivation -you want to be healthy and happy for them, and you want to set tgem a good example. Weight loss doesn't have to be obsessive or unhealthy- if you think of your children as a motivation rather than an excuse to not do it, you might be more inclined to do it in a more sustainable and healthy way.
There are many ways to lose weight, I like calories counting because it is idiot proof, I don't go off track if I eat a certain food and it makes me think about my portions and snacking, which were my big downfall. It naturally makes me eat better, because you get more bang for your buck with veg and lean protein, but I can eat treats if I factor them in.
Some people prefer other methods, fasting diets etc. They won't work for me because they are too faddy and would make me too frustrated and obsessive, but for some they are excellent. you just need to find what works for you.
oh, and walk everywhere and find exercise that doesn't feel like a chore to you. mine is dancing to YouTube videos 
those tutorials make me sweat loads.
good luck