Is the widow and her minor children obliged to visit the deceased husband's family, especially given the disagreements, insults, and accusations of alienating the children? And who is responsible for inquiring about whom?

You are not obliged to visit your in-laws, nor to take your minor children to visit them, especially if doing so causes you harm or embarrassment. You bear no sin for any estrangement on the part of their paternal family as long as you are not the cause of it, and you do not prevent them from connecting with or communicating with their children. Similarly, your in-laws are not permitted to harm you without a legitimate Shar'i right, for "And those who harm believing men and believing women undeservedly have certainly burdened themselves with slander and manifest sin." It is advisable to reconcile with your in-laws and treat them kindly, welcoming them if they wish to connect with their children, for "Reconciliation is best."