public void Update(UpdateParentModel model)
{
    var existingParent = _dbContext.Parents
        .Where(p => p.Id == model.Id)
        .Include(p => p.Children)
        .SingleOrDefault();

    if (existingParent != null)
    {
        // Update parent
        _dbContext.Entry(existingParent).CurrentValues.SetValues(model);

        // Delete children
        foreach (var existingChild in existingParent.Children.ToList())
        {
            if (!model.Children.Any(c => c.Id == existingChild.Id))
                _dbContext.Children.Remove(existingChild);
        }

        // Update and Insert children
        foreach (var childModel in model.Children)
        {
            var existingChild = existingParent.Children
                .Where(c => c.Id == childModel.Id)
                .SingleOrDefault();

            if (existingChild != null)
                // Update child
                _dbContext.Entry(existingChild).CurrentValues.SetValues(childModel);
            else
            {
                // Insert child
                var newChild = new Child
                {
                    Data = childModel.Data,
                    //...
                };
                existingParent.Children.Add(newChild);
            }
        }

        _dbContext.SaveChanges();
    }
}