How can I find out if a malpractice lawsuit was filed or a settlement was made on behalf of my daughter who lives with me?

If you know in which court the lawsuit may have been filed, you can go to the court and look in the court's computer.  Look in the plaintiff/defendant index to try to find the case.  If you look under plaintiffs, look for the father's name.  If you look under defendants, look for the name of the party who was sued in the malpractice case.  When you find the case, give the case number to the court clerk and the court clerk will let you see the file.  You can't remove the file from the court, but can ask the court clerk to photocopy it for you.  If you don't know in which court the case was filed, since it was malpractice it was probably filed in Superior Court located either where the father lives or where your daughter lives.  Your state may have a different name for Superior Court.  If a lawsuit was filed, then there wasn't any settlement prior to filing the lawsuit.

If your daughter is a minor and the case was settled, there would still be a court record because in the case of a minor, there is a court proceeding called a minor's compromise to have the funds from the settlement set aside for your daughter.  Again, you would look in the court's computer for the case with the father's name to obtain the case number.