LINQ: How to get items from an inner list into one list?

You can string a couple queries together, using SelectMany and Where.

var selectedChildren = (from p in parents
                       where p.Children.Any (c => c.CategoryNumber==1)
                       select p)
                       .SelectMany(p => p.Children)
                       .Where(c => c.CategoryNumber == 2);

// or...

var selectedChildren = parents
                         .Where(p => p.Children.Any(c => c.CategoryNumber == 1))
                         .SelectMany(p => p.Children)
                         .Where(c => c.CategoryNumber == 2);