I am a married woman who committed adultery and I have also informed my husband about it. We have children together and I am seeking a solution for this difficult situation. Is it allowed for my husband to forgive me for the sake of our children?
Bismhi ta'ala
This is going to be a choice the husband makes. Of course, you must understand how difficult it would be for him to trust you again, or to forget the incident, and it might continue to be brought up, especially if you have an argument.
He might even accuse the children of not being his, and so on.
Therefore, if he forgives you, which is possible from a shar'i perspective, you must both navigate correct solutions to deal with the infidelity and how to avoid it in future, from both sides.
And Allah knows best