Is the claimant considered to be unjust to her children by marrying and leaving them in their father's custody, and is her ex-husband entitled to prevent them from communicating with her more than once a week?

You are not being unjust to your children by marrying and leaving them with their father, for there is no neglect involved in that, especially since adult, mature children are not subject to custody, and they have the choice to reside with whichever of their parents they wish. It is obligatory for children to honor their parents, and their father has no right to prevent them from contacting you or visiting you. Obedience to him in this matter is not obligatory, and it is permissible for them to visit you and contact you without his permission. They should strive to combine honoring you and honoring their father as much as they are able.