Hi! There have been a lot of negative comments from people who obviously have never dealt with anything like this - ignore them! You sound like a wonderful mom who's going out your way to help your kids make healthy choices and be there for them and spend time with them, that's a lot more than most parents can say! So kudos to you!
My mum was in shape then got quite heavy after having kids and I saw how much it impacted her self esteem, her friendships, and even her energy on a daily basis. She always spoke negatively about herself and I think that had much more of an impact on us than her actual weight. She had a really hard time staying motivated to lose weight and the ups and downs of dieting didn't help her self esteem. As someone who's been the child in this, I'd say the biggest thing to keep in mind is not to talk down about yourself!
Some people have recommended saying "I make unhealthy choices so I'm heavy" - not sure that's the way to go with a child, it will always make them of think of you as less than other people and might make them worry about you as they think you're unhealthy. I wish I just heard everyone has different bodies and different qualities, some of us are small, some of us are big, and we all have something special to share that's what makes us unique and different. If we had seen my mom as confident while she was heavier (I'm talking decades) I think it would have instilled more confidence in us (although we're all healthy weights) and would have made us worry about her less.
In the meantime, without it being a discussion with your children, I really would try to find a sustainable way to get healthier! It's not about how you look, but how you feel as your kids get older! I saw how much losing weight made my mom more accessible to us, helped her feel good and confident and outgoing, and these things trickle down into every day life. It's been so wonderful to feel like I have my mom back at 32. Not because of how she looks, I couldn't care less! But because it's obviously made her happier and we feel that happiness when we're with her.
I hope you feel supported and know you really do sound like a wonderful mum!