[c++] How can I initialize C++ object member variables in the constructor?

You're trying to create a ThingOne by using operator= which isn't going to work (incorrect syntax). Also, you're using a class name as a variable name, that is, ThingOne* ThingOne. Firstly, let's fix the variable names:

private:
    ThingOne* t1;
    ThingTwo* t2;

Since these are pointers, they must point to something. If the object hasn't been constructed yet, you'll need to do so explicitly with new in your BigMommaClass constructor:

BigMommaClass::BigMommaClass(int n1, int n2)
{
    t1 = new ThingOne(100);
    t2 = new ThingTwo(n1, n2);
}

Generally initializer lists are preferred for construction however, so it will look like:

BigMommaClass::BigMommaClass(int n1, int n2)
    : t1(new ThingOne(100)), t2(new ThingTwo(n1, n2))
{ }