Your feelings changed after she introduced her opinion. So, your feelings fluctuated because your thoughts fluctuated given her influence. But the facts of your circumstances didn't change, did they?
Others don't live inside your skin. Given your circumstances, they only wholeheartedly imagine what they'd do, but were they to step into your circumstances and live it themselves, with all the thoughts and emotions that go with it, who knows what they'd really do? They're not you, and you're not them. Your kids don't like your H... is it any wonder they'll suggest ending it with him? You, on the other hand, love him. You're the one in a relationship with him, not your children.
Maybe you can recognize that your children's opinions have an influence on you, but they're only their opinions. Ask yourself: Is it healthy to bounce your life around depending on what any others may think? Ask 100 people that you trust closely, and you'll get 100 different answers. Is it realistic to take everyone's advice? Why wouldn't the same be true if you only have a couple of opinions instead?
Concerns that they won't respect you, or that they'll change their mind once they see you happy, are unnecessarily pressing on your mind. Your children do, in fact, have many reasons to respect you and have always respected you, and will not toss out all their respect simply because of what you have chosen to do regarding your own husband.
But if they don't respect your decisions in this instance, or if they don't accept what you're doing right now, the problem really is with them and not you.
If indeed it turns out that your relationship doesn't work out, you'll know it, and trust yourself that you'll do right by you. You're not a battered wife, you have many good reasons to work on your relationship, you're making improvements all the time, things remain positive for you.